I'm no longer using X/Twitter, so I can't verify this for myself, but someone on Bluesky says that likes weren't literally made private, they just removed the button - you can still see them by adding "/likes" after someone's profile URL.
This is about what you would expect from a site that runs entirely on Elon Musk's whims and has a lot fewer engineers than it used to.
(The quote in the NBC News article can probably be decoded as "Don't worry, you can now privately let all your favorite white supremacist posters know how much you like them.")