
No Jewish ancestry is required to convert. Converts can sometimes experience discrimination but this is against Jewish law and contrary to how God commanded us to treat converts. What can also happen is if any of the rabbis who oversee your conversion are not fully observant then your conversion may not be recognized as valid by some group. The most common situation where this occurs is if you convert in a Reform community your conversion will likely not be recognized by Orthodox communities.
There’s no getting around this though since even if you do a completely by the book Orthodox conversion, maybe in six years one of the rabbis who oversaw it is exposed for occasionally indulging in a cheeseburger, anyone who doesn’t like you can use this to call your conversion into question. It’s not a perfect system but it’s managed by humans, so it can’t ever be. TLDR no, anyone who is committed can convert and be fully Jewish under the law.
I agree it’d be very rare for a conversion to be declared invalid by a beit din in a community that you’ve been a part of for a while, they would probably just reconvert you if they knew you were observant if there was a legitimate question, it’d take like a week. But if you’re a convert and you move somewhere new, it’s always a possibility that your conversion’s validity will be questioned even if it was giyur k’halakha. It’s annoying but it’s kind of just the lived reality for some converts.
I mean I feel like this is just known? Several of my friends have been raised Jewish, sometimes with everyone in their family being Jewish going back two or three generations, but Chabad still doesn’t consider them Jewish because maternal grandmother did a Reform conversion or something. It’s not very community or every convert but it does happen.