Jeff, I believe you're correct in that most come here to be Americans, They can do so without any requirement to change their religion, their cultural heritage (as long as it stays within the laws of the U.S.) and their beliefs. That is their right as citizens of this country. What I find disturbing is the recent and growing trend to be associated with their former country of residence and an also increasing vocal displeasure with the country they have settled in to the point of demonstrations or outright violent activity. That's not ALL immigrants but lately a fast growing number. They surely don't want to leave but it seems they don't want to be American either.
Another issue, closely allied with the former, are groups who demand to be addressed as only part American, in combination with their ex-patriated country, even if it has been several generations past. The groups, [fill-in-the-blank] / Americans, be it Italian, Polish, African, etc want their former home country included there or the rest of us are racist or at the very least politically incorrect (too bad on that one). Case in point: I am of Welsh descent (now no one will talk to me !!) but I do not refer to myself as a Welsh-American. To a Hispanic or black person I'm a 'white guy'. Yet, many of the black population of the U.S. take offense to a similar appellation ("I'm African-American"). If I ask them to then refer to me as a Welsh-American, they look at me like I've got three heads. "You're white, man", but they're insulted if I refer to a 'black' guy.
Why do you suppose this reaction to simply being an 'American' exists? A need to stand out, a need to be an exclusive group, or a need to disassociate? Whatever it is, it didn't used to exist as immigrants were eager to be simply American, in years past. As I said, it's their right to harbor these opinions but I find disruptive of a cohesive society. You opinion?