I certainly know good Catholics who register as Democrats, but while I’m not going to engage in an argument, I’m just going to relate my personal experience.
I registered as a Republican for a single election when I was first old enough to vote, which is now a long time ago (Reagan was running for a second term). Thereafter I registered as a Democrat and was one for over two decades. I even briefly held a local Democratic elected party position.
Then I dropped out about two elections ago and switched to the GOP. Due to other positions the GOP holds locally, and because I am genuinely more to the left than the GOP is on many issues, I dropped out of that and registered as an independent. Last Presidential election I cast my vote for the candidates from the American Solidarity Party.
So for me, while I understand others feel differently, I could personally no longer be a member of a party that was basically for abortion on demand and which was become deeply opposed to recognizing that human nature has a biological nature, including as part of that, actual genders.