There have always been qualms about the Sentinels.
Mutants aren't terribly popular with the general population, but even some of the most virulently anti-mutant occasionally had qualms, at the beginning, about sending metal creatures taller than a man to round up the mutants for registry and containment. The government said it was because the Sentinels had the ability to counter mutants' unnatural abilities, and it would be insane to send a human who might get hurt instead.
And then there was a coup. Plenty of people would have had qualms about the fall of democracy even if it hadn't involved mutants being executed on sight instead of quietly ushered off to the land of plausible deniability. Mutants might have different skin and hair than normal humans, but they looked pretty much the same as anyone else once reduced to a smear of burnt flesh and shattered bone.
And then it wasn't just mutants, but those who were accused of sheltering them, and then those who were suspected of having pro-mutant sympathies such that they would shelter them if it came up.