Short version: If Congress ratifies a treaty that restricts Constitutional right of citizens, is the treaty Constitutional? Opinions vary, but the weight of legal scholarship is no, it isn’t. The problem is that the Constitution does give special weight to treaties, calling them the “supreme law of the land.” The issue isn’t can Congress abrogate such a treaty - of course it can (as can the President). The issue is can we as citizens challenge such a treaty on Constitutional grounds.
The issue often comes up in the context of the ban on small arms that the UN is trying to push in the form of a set of treaties. Google/yahoo treaty constitution small arms UN or something similar and you’ll see what I’m talking about.
Well if the UN or anyone else for that matter want my arms all they have to do is come for them. I will surrender them willingly, ammo first of course!