Alex did cross the WGA picket line during the 2007-08 writers' strike, and the show used recycled clues during that time (they were about 10 years old). The difference is that social media apps like Twitter and Reddit weren't around for people to make a big deal about it. (Also, Alex was never on social media himself, unlike Ken.)
Ken went into more detail in a thread on the Facebook group devoted to his podcast, confirming that he is a member of SAG-AFTRA, that he's been in contact with union leadership, and they've specifically indicated that he should work, because their strike doesn't cover "Jeopardy!" and because Ken has a pre-existing contract with the show. Presumably, Mayim was able to opt to not cross the WGA picket line because she has a different contract with the show, possibly related to the fact that she's only employed as a host, while Ken is also technically a member of the production staff.
(Left unsaid was the fact that if Ken doesn't work and the show has to cancel tapings, it affects the crew members who are members of the IATSE union. Ken did acknowledge that it's a no-win situation.)