Based on my own experience, I think this is over-generalization that is mostly false. Most Eastern European immigrants are not political but economic - they come here to strike it rich and babble anti-communist mantras because these are the magic words that get them their I-94s and green cards. Most of them plan to stay here for a few years, make a boat load of money and come back as rich and respected men. I use the word men deliberately, because women have a somewhat different experience (more about it in a moment).
The virulent anti-communism many of them develop is result of several factors. First immigrant communities are often already reactionary, so the stuff is already in the air. But more importantly, many of those fellows left quite comfortable lives behind, jobs, houses, farms etc. which they gave up with immigration. So if their dream of the American riches does not come true, and they end cleaning toilets or flipping burgers at minimum wages - they cannot go back because they would loose status and respect of their former neighbors - for they would come defeated. Virulent anti-communism saves their faces - they may be cleaning toilets here but they will not go back, they say, because of "political oppression" which btw they never experienced. But after telling that story many times, they actually believe it.
Women, however, are often an exception. They genuinely want to stay here even doing menial jobs because they genuinely fear repression if they return. Not political, though, but social. EE tends to be fairly patriarchal, especially outside major urban centers. If these women returned, they would have to give a lot of freedoms that here are taken for granted: freedom to dress any way they want, freedom to spend their own money and time any way they want, freedom not be married and sleep with whoever they want, or freedom to call the cops on their abusive husbands. Although this changed quite considerably during the past 30-50 years , mainly as a result of socialist policies, this patriarchal crap is deeply ingrained in EE social fabric and right now is being dug up by fascist and clerical elements as a reaction to socialism.
Another important aspect is that immigration offers a very interesting experiment that reveals something about the nature of political and ideological preferences. Often ardent supported of the communist regimes in EE, ex-party apparatchiks etc, become ardent supporters of GOP and right wing here. My explanation of that "switch" is that political ideology is not a matter of rational choice but a cognitive process of "sense making." The cognitive process of sense making is organizing various experiences into meaningful wholes (there is a ton of literature on that under the rubric of cognitive psychology and sociology), or creating order in the chaos, if you will. Cognitive psychologists talk about two different styles in so doing - one is the rigid adherence to the conventional norms of the society and the status quo, the other one based on a flexible application of principles.
People who have a natural inclination toward the first cognitive style will adhere to whatever conventional norms and political structures surround them - they are devout communists under the Soviet regime, ardent GOPniks in the US, staunch Afrikaners in the apartheid South Africa - in a word, pro-establishment in any country or society in which they find themselves. Again, this has nothing to do with their status as immigrants but with their natural cognitive predisposition - immigration merely reveal their chameleon-like ability to blend in with the status quo.
Wojtek