Not exactly. Although historically up until 2000, it was much more likely for a Democrat to change parties than a Republican. Since then, things have begun to shift to be more equal between the parties. Compiling the numbers since Trump took office in 2017, as those seem more relevant to modern politics:
Democrat -> Republican (14)
Democrat -> Other (9)
Republican -> Democrat (19)
Republican -> Other (15)
At this point in history, the tables have turned and Republicans are seeing more departures. But I suspect this trend will end after Trump leaves office.
Sorry, I should have been more specific with my language: instead of "politicians" I should have said "Congressmen." My understanding is that a Rep->Dem switch has only happened four times, while a Dem -> Rep change has occurred 18 times.
Tbh I'm not 100% on what caucusing means, so maybe I should research it a bit more before commenting.
A "caucus" (in this context) basically means gathering of like-minded folks for purposes of planning/strategizing. "What policies do we want to push, and how do we want to accomplish that" is done much more efficiently by a group that can agree on a decision-making process, so while it's theoretically possible to not caucus at all you're probably not going to accomplish much, outside of somehow being the only deciding vote on a matter.
For the record, you can belong to multiple caucuses at once, and I'm pretty sure every Congressman is part of at least two caucuses.