I have a problem with their position on synths, but I have a bigger problem with their position on ghouls. The former at least makes sense to me, the latter just strikes me as prejudice for the sake of it.
The ferals, which they wipe out, or the sentients, which they don't like but ignore?
There's plenty of reason to hate ferals- starting with that they're basically mindless zombies that will attack anyone. Feral ghouls are a public menace to everyone.
There's less reason to for their prejudice against non-ferals- but at the same time, there's less action. It's a perfectly legitimate worry for the future, but the Brotherhood hasn't exactly done anything to non-feral ghoul communities that we can point to.
Sure, racism is bad, but it's hard to argue against results- as a faction, the Brotherhood does the most good for everyone in the Commonwealth, including the sentient ghouls. They're the only major faction that's proactively fighting the public menaces- purging the super mutants, feral ghouls, and even knocking out raiders. These are the real threats to the Commonwealth, and the BoS is the only one actively seeking them out.
The Minutemen are nice, but ultimately defensive and reactionary rather than proactive. The Institute is pretty amoral and self-interested, and has only really helped the Commonwealth by accident while defending their own interests. The Railroad doesn't really care about anyone but Synths, and the ensure the end of the Synth race by blowing up the means of their creation anyways.
If you want to remove the greatest dangers from the most people in the shortest amount of time, the Brotherhood is where you're at. Anyone else is pretty much counting acceptable casualties in hopes things are nicer or better in the future. (Which is fine, but let's not make false-equivalences.)