The fact that politics are more divisive now than in 1937 is an argument FOR trying to expand the Court. No Democrat is going to vote GOP just because they don’t like the idea of expanding the Court, so the potential political downside is much less.
As an aside, we don’t actually know how popular or unpopular Roosevelt’s plan was, since modern opinion polling didn’t exist then. We know that political elites of both parties were opposed to it, but we don’t know how ordinary voters felt. The only evidence we have to go on is the fact that they re-elected Roosevelt twice by enormous margins. I’d be happy to repeat that history.