Akuperma, actually intermarriage has only been widespread for two generations with the exception of pre-Nazi Germany where it was already two or three – and they assimilated completely into Xtian society.
ZD, why is that a problem? One the person learns a bit he will discover that he is not really Jewish and convert. I have several such friends.
CA, no we won’t. Mi shenitma nitma (once a mamzer has melded into the general Jewish community his problem is forgotten – SA EH 2:5). According to Rabbi Yossi even known mamazerim will be purified. Rabbi Meir disagrees (Kiddushin 72b). In a machloket between Rabbi Yossi and Rabbi Meir we pasken like Rabbi Yossi.