I think it's just a case of once bitten, twice shy. The mutants come from NCR territory, and I think it's a fair assumption that every last one of them encountered bigotry and xenophobia there at the very least, if not outright hostility. It's understandable... the stereotype of the violent, dangerous mutant isn't a groundless one, and in a harsh world, people would rather deal directly with a perceived threat than take a risk on being morally upright and possibly getting themselves killed. It's not right, but it happened, and I'm sure it left a pretty bad taste in their mouths.
I personally wouldn't put the blame on NCR's shoulders but on human nature. If the Mutants had originated in Caesar's lands, they'd likely have been persecuted there, too (unless he embraced them as elites, but I'm honestly not sure whether that would jive with his "back to basics, humanity re-ascendant" creed), and they'd bear his Empire ill-will. If they'd come from Sheboygan, Wisconsin, they would've suffered at the hands of the Sheboyganites and they'd be leery of them.
NCR brings civilization. Civilization brings people. People, defaulting to the lowest common denominator as they so often do, bring problems for mutants. To me, it's as simple as that. The plight of the mutants in NCR is similar to the plight of minorities during the American civil rights movement... there are a lot of friendly faces around, a lot of people who believe in their cause and who actively work to further their station in the world (and in that regard it could be rightly claimed that the NCR is more mutie-friendly than most), but the forward-thinkers are vastly outnumbered by the bigoted asshats.
