The Halacha follows Rabbi Yehoshua that a Mamzer is only if one marries an Erva that is Chayav Kares.
The Halacha follows the opinion that the descendants of a non-Jew living with a Jewess are Kosher Jews and not Mamzerim.
Now, there are opinions arguing both points. Rabbi Akiva says that anyone who's a result of an intimacy which violates a simple negative commandment is also a Kares. There are a few opinions (in Yevamos) which hold that the descendant of a non-Jew with a Jewess are Mamzerim.
Now, someone offers a Shidduch to my friend. Would it be Halachically acceptable to advise him not to marry those people, despite the Gemara/Rishonim/Shulchan Aruch clearly permitting them, as perhaps Mashiach would come, a Sanhedrin would reconvene, and perhaps rule like Rabbi Akiva/The other opinions.
What about if there was a piece of Chelev about which there was a debate, and the Halacha got ruled that it's Kosher. Is it still acceptable to not eat it (and to tell others not to), as perhaps the sages Gemara made a mistake, and when Moshiach would come and a Sanhedrin would be restored we would all have to bring a Korban Chatas (note, I'm assuming most Jews didn't eat this particular cut of meat so there would be no Par Helem Davar Shel Tzibbur).