Note: There are also claims that it was modern-day Karnataka people who descended from Satavahanas and not Andhra-Telangana people.
Who are the Satavahanas:
As mentioned in the previous section, Satavanahas were a dynasty that ruled the Deccan regions between 2nd century BC and 2nd century AD. They seemed to have risen to prominence after the downfall of the Mauryan empire. Their administrative language was Prakrit. Most of their literature that is available to us is in Prakrit. The earliest Telugu and Kannada inscriptions found in India are dated back to the period of Satavanahas, so the claim for ancestry from both language speakers. Then comes the interesting part.
Satavanahas were strong proponents of Vedic culture. They considered Vedas divine. They exalted Brahmins (they considered themselves Brahmins too) and were the first to practice the custom of donating tax-free land to Brahmins in South India. Brahmins occupied the highest status in the social ladder and enjoyed great privileges. (Note: Satavahanas seem to have patronised Buddhism too to some extent.)
Satavanahas were the first to introduce and practice the Varna system in south India. They also seem to have followed the laws of Manusmriti. B.R. Ambedkar even stated that the Manusmriti was compiled during the Satavanaha period.
SS Rajamouli, the director of Baahubali tweeted this in October 2012. This was probably the time he was researching the movie and you can see him making a case for Manusmriti in his tweet. One more reason to believe that Baahubali was indeed the story of Satavahanas.

Some more parallels between Satavahanas and Mahishmati:
1. Satvahanas kings held their mothers in high esteem. They even annexed their mother's names with their own. Examples: Gautamiputra Satarkarni, Vashisthiputra Satarkarni, etc. Through Baahubali, women play a major role. Ex: The characters of Sivagami, Devasena.
2. The most well known female Satavahana is Nayanika. She was a queen to Satarkarni I, one of the most famous Satavahana kings. She is credited with Nanaghati inscriptions and is said to have acted as a regency to two of Satarkarni's young sons. The character of Sivagami seems to have drawn inspirations from her.
3. The Satavahanas were in constant clash with the Western Satraps (Saka) and even lost their kingdom to their rivals between 50-100 CE. This period is known as the Kshatrapa interregnum. In the movie, there was a Ballala interregnum.
Who are the Pindaris:
We are introduced to the Pindaris in Baahubali 2. While Kattappa and the elder Baahubali are visiting the various kingdoms within their empire, they stop for water at a lake by a village only to find that the entire village had been massacred and all the villagers drowned in the lake. Kattappa remarks that this is the work of Pindaris.
We again encounter the Pindaris in the Kundhala palace. TheKatappa, elder Baahubali and Devasena join hands to defeat them.
Who are these pindaris?
They have to be western Satraps also known as the Sakas (Indo-Scythians). The map below shows the extent of the Western Satrap kingdom. It can be seen the Western Satrap shared their boundary with the Kundhala kingdom. The Satavahanas and the Sakas were in a constant clash for over 200 years. They fought 2 full-fledged wars with each other, winning one each. The Sakas were split into many clans, one of them being the apasakas or apasiakas meaning water Sakas
History tells us that the western satraps were civilised people who migrated into India from modern day Iran (hence the name Scythians and Sakas). However, the movie portrays them to brutal killers and foragers. Why? The answer lies in the religious beliefs of Satavahanas. We already saw that the Satavahanas were followers of Vedic culture. According to the Vedas, any culture that was not Vedic in nature was impure, uncouth and less civilised. The people who belonged to these foreign cultures were considered as Mlecchas. A term that is used to refer to immoral or inferior people. We know that Sakas were immigrants. To Satvahanasm, Sakas would have been inferior, less civilised people who were brutal savages.

(Note: The Pandya kingdom shown in the above map is incorrect.)
There can be an alternate explanation too. Pindari was a term used to refer to 18th-century Mughal soldiers who after being defeated in battle by the Marathas, foraged Maratha cities as agents for Maratha rulers. They would get a small percent of the spoils.
So, it is possible the movie combined the traits of Water-Sakas with the Pindaris of the 18th-century for its portrayal of Pindaris. According to the adherents of Vedic culture, both Scythians and Mughals would have considered mlecchas and therefore were inferior. Two birds with a stone.
Why Kalakeyas:
We saw earlier that the movies imply that Tamils were Kalakeyas. Why was this done? Simply to realise Nasik Prasasti.
Nasik Prasasti is the eulogy of Gautamiputra Satarkarni. Nasik Prasasti states that Gautamiputra Satarkarni ruled over the entire southern peninsula including modern-day Tamil Nadu and Kerala. Nasik Prasasti states that Gautamiputra's horses drank water from the three oceans (Indian ocean, Arabian sea, Bay of Bengal). This literary device implies that the Satavahanas ruled over Tamil Nadu and Kerala. History tells us otherwise. Satavahanas never ruled over these lands. However, the movie uses this as a plot device and in doing so distorts the history of TN and Kerala.
So, if the Kalakeyas were simply a plot device, why show them as primitive barbarians?
Once again, the religious outlook of Satavahanas comes into play. Satavahanas were followers of Brahminism while Jainism and Buddhism were thriving in TN and Kerala during the Satavahana period. The other reason would be the language divide. Similar to religions, languages were fighting for space then. New languages emerged and old languages died. Telugu and Kannada arrived on the scene. Tamil was losing its foothold in the Deccan region. By making Kalakeyas speak a primitive language, was the movie trying to imply that Tamil was primitive then? I wouldn't be surprised if this was done on purpose. A few hundred years down the line when history, myth, legend and fiction writes a new history, Baahubali might play a part in tarnishing the Tamils who have always opposed hindutva.
Note: In modern-day South India, TN and Kerala are two states that resisted the incorporation of Vedic culture and Varna system into their culture. These are the two states in South India that have a comparatively larger percentage of the Christian population. These were people who stood up against untouchability and caste system Hinduism imposed on them.
Baahubali and hindutva:
A couple of days after Baahubali 2 hit the screens, one of the facebook pages with hindutva ideologies and RSS affiliations (Page is titled "Students against corruption), put up the following post.

A rough translation: The success of the Baahubali 2 is a victory for hindutva. Rajamouli has beautifully portrayed the essence of hindutva that can work today. The Ganesha chariot scene was exhilarating. Killing the asura while sitting on top of an elephant was brilliant. The Krishna song was highly moving. Opposing the empire to keep a promise is hindutva. Making a promise on Shiva indicates the sovereignty of Bharath. As the end card rolls, the song on Shiva in the background as the lingam bathes in the waterfall gave goosebumps. Please watch the movie in theatres. That is the least we could do for the man who spent crores to spread and uphold the principles of hindutva.
1. The Indo-Iranians and Mughals became Pindaris.
2. The Jainist and Buddist became Kalakeyas.
3. "Karikala" Kattapa became a slave.
4. Even Bahubali (if you know who I mean) was carrying a linga around.
And that is the problem with Baahubali. By portraying all other foreign cultures and religions inferior, uncivilised or brutal, Baahubali has shone a bright light on hindutva. And by being successful and accessible to the masses, it has laid down a path for everyone else to distort history as they please.
The real history:
1. The western satraps were not uncivilised people. They were not brutes. They followed Hinduism and Buddhism and spoke Sanskrit, Prakrit, and other Indo-European languages.
2. The Satvahanas were not the only civilised people in the region. Long before them, multiple and sophisticated civilisations had been founded and destroyed.
3. The Kalakeyas who are told be inhabitants of the south were not a primitive race. Their language was not primitive either. The areas south of the Satavahana empire were ruled by three Tamil dynasties. One among them, Pandyas, were a lot older than the Satavahana empire. Cholas and Chera arrived on scene a few centuries before the Satavahanas.
4. The areas that lay south of Satvahanas was not forested land. They were inhabited by Tamils for long. The recent excavation at Keezhadi dates the civilisation that existed in modern day TN to 500 B.C. And it was a sophisticated civilisation with trade links Roman empire.
5. Not all cultures foreign to Vedic culture were inferior. And Vedic culture itself was no less savage for its times.
The conclusion:
As a fantasy, Baahubali is a cinematic masterpiece. However, once the underlying historical references become apparent and an agenda, planned or unplanned, start to emerge, you start questioning the motives of its creator. If one reads between the lines, it becomes apparent, Rajamouli was trying to glorify the Satavahanas while belittling the rest of the country, distorting history as he does it.

The historic legacy of the Satavahanas was not enough for Rajamouli. He wanted a taller and a mightier one. He did not bother if he belittled others in the process.
Further Reading:
1. Satavahana dynasty
2. The Satavahanas
3. Socio-economic conditions of Satavahanas
4. Western Satraps
5. Pindaris
Ps. This article does not intend to offend any dynasty, language, region, religion or caste.
Addendum 1 (May 24, 2017):
The following is a part of an answer detailing the history behind Baahubali. It can be found in quora.
As you can see, the slander has begun. I don't know if the caste of Kattappa was mentioned anywhere in the movie. Yet here is someone claiming to know it and he is also presenting a history for the same.
How did he make this connection?
First about the Nadars,
1. Nadars were a backward/suppressed caste in TN before independence.
2. They were considered inferior by other forward castes (not just Brahmins) and were denied entry into temples until 1930's.
3. Women from the caste, much like women from the Ezhava caste in Kerala, were forbidden from wearing upper garments. Their breasts were to be left bare and based on the size of the breasts, their families were taxed.
4. Suppressed by the hindus for long, these a sizable population converted to christianity in the 18th/19th century. These were one the first groups of people in Tamil Nadu to embrace christianity.
Now, if the caste of Kattappa isn't mentioned or implied in the movie, how did this post come to think the caste of Kattappa is Nadar? I think that's simple. The Nadar folks go around claiming that they are the descendants of ancient Tamil kings when there is no shred of evidence to conclude the same.
So the author of this post made up this link: Karikala Katappa - Karikala Cholan - Descendents of Cholas. He assumed Nadars were the descendants of Cholas. They are not. He then puts a note clariying things, but soon someone will make a connection that Nadars were backward caste, so they could have been slaves. And if they are descendants of Tamil kings, someone will come to a conclusion that Tamil kings were once slaves to Satavahanas.
Real history: Ancient Tamil kings were not slaves to Satavahaas.
Rajamouli has done his job to perfection. He has tarnished Tamils and he has served Hindutva well.
(Clarification (May 25, 2017) : In the first movie, Kattappa is introduced as Karikala Kattappa Nagar or Nadar.)
Nagar were the people who are said to have lived throughout India and Srilanka during the times of Mahabharata. Ambedkar claims that Nagars spoke Proto-dravidian, which is nothing but Proto-Tamil.
The other reference could be to Nagarjuna, the buddhist monk who is considered as one of the most important Mahaya Philosophers. He is considered to have lived between 150CE to 250CE. Possibly during the Satavahana period.