This is very much not the case. What's closer to truth is that the discussion moved on from a framework laymen can seemingly understand conclusions, to one where conclusions (or their implications on mathematics proper) are a lot harder to explain to laymen. Foundational work is still a thing, but I don't think it affects the nature of mathematics in a way laymen can conceptualize.
Take Godel's incompleteness. People say it's something laymen can understand, and people attempt explaining it to masses every day in youtube, reddit etc. But if you truly get into the formal conclusion (i.e. with Rosser's trick, the conclusion is: "a theory cannot be an extension of Q, complete and consistent all 3 at the same time") you'll see that it's already pretty far away from what laymen thought they understood. And modern foundational work exponentially drifted away from this too.
I'm not a mathematician so everything in this comment should be taken with a grain of salt.