(I can’t speak to Einstein’s views on communism specifically, given that much of what I know of his political views in this vein comes from his essay “Why Socialism?”. He may well have been a raging commie, but chose Socialism because he was aiming his piece at a particular audience.)

He already had to leave one country before, it's probably more him being careful.

The FBI had opened its file on Einstein in 1932, , when he was seeking to immigrate to the United States, with a long report by the Woman Patriot Corporation (WPC), which in its extreme anti-Communism, claimed that Einstein was inadmissible to the country. “Not even Stalin himself,” the WPC charged, “is affiliated with so many anarcho-communist international groups to promote…world revolution and ultimate anarchy, as ALBERT EINSTEIN.”3 The FBI continued to collect everything it could on Einstein’s numerous socialist connections for the remainder of his life.

Couldn't work on the atomic bomb bcs the military considered him a security risk.
Nobody is going to out themselves as communist in those circumstances