Frankly, the way things are now in the comic-book Marvel U., you'd think people would love mutants compared to Inhumans--the idea of a cloud of mist suddenly flowing through your neighborhood and changing you into a freak who is supposed to respect some monarchy you've never had any relationship to before would be vastly more terrifying and infuriating to most human beings than the idea of mysteriously changing at adolescence, when you change anyway. Terrigen in the current mythos is like toxic waste: the citizens of the world should have long since demanded that the entire hierarchy of Attilan be attacked by a UN military force and detained for crimes against the world. The way the story's being told at the moment, that wouldn't be bigotry, it would be righteous retaliation for a war crime.
The main differences are the terrigen cloud as far as the general population (and like 99% of the inhuman one) was a horrible accident/tragedy due to Thanos' invasion at the time and the Royal family/Inhuman nation is doing it's best to mitigate and work with the affected countries and populations. The Inhuman nation is taking in any willing 'NuHuman' but it's not forcing them to fall in line with their monarchy. Even if/when the truth comes out, it wasn't an action by the Inhuman nation, but rather the individual action of one man who has since been removed from power. Another factor is the terrigen cloud is something you can avoid (or seek out), where mutation just happens. One of the general plots of one of the inhuman books currently is about a official response team that follows the clouds around helping anyone who is changed and working with the local governments and populace to mitigate any fallout.
On the mutant end of the spectrum you either have extreme radicals hell bent on wiping out baseline humanity or on the 'better' end you have child soldiers waging a secret war and using their vast resources to manipulate multiple levels of government and industry to their advantage.
Like sure, the Marvel Worlds in-universe hatred and racism towards mutants is down right comical at times, but it's not that hard to see why the Inhumans might be better received then Mutants would.