Danse seems like the type to be a fanatic of the first ideology presented to him, yes.
All the Synths you meet in FO4 are and imo it's not even wholly by design but rather that the Institute can only 'program' in so much of their personalities with the rest being formed by impression i.e. the Synth sent to replace a gangster becomes not just a gangster by 'profession' but by 'religion,' with the same happening with Danse and the BoS in that he is perfectly willing to let you end his life as the Brotherhood wills, but if you convince Maxson to spare him even as he gets officially kicked out of the BoS... he's perfectly fine with that since you and Maxson are BoS and he's not so he has no say.
Question: did the E-USA kill / destroy all the existing Synths (or at least those they could catch) or did they come to some arrangement? And since it's Fallout I can't imagine there isn't some Institute inspired E-USA group going further and further into Institute flavored mad science considering how the setting breeds S.P.E.C.I.A.L. people who don't just survive, but thrive.
Most "bunker people" groups are highly xenophobic - see Vault City, the Boomers, Vault 101, the Institute - but I would call the BOS elitist as their ideology possesses the factor that they are the only group fit to wield advanced technology, and they have a duty to control its use (usually by killing other highly-advanced groups and taking their stuff). They dislike "primitive wastelanders" less than they dislike other advanced groups - the former brings contempt, the latter outright hatred.
That's a fair point, but I'd still argue that that mentality is encapsulated in their bog standard tribalism since outside of the canon FO3 DC Brotherhood which was pushed to OOC / Sue levels of friendliness because they straight up disallowed the Lone Wanderer to side with any Enclave other than President Skynet, the BoS simply doesn't see the wastelanders as kin to them while the NCR / E-USA and etc. are other tribes that are actual or potential enemies. But unless their internal culture has radically shifted, inside the Chapters themselves and between Chapters they are pretty egalitarian within their chain of command until you get to the mad scientists like Father Elijah.
At most I'd say the Midwest BoS are 'de facto' elitists since they were forced by circumstance to take control of the wastelander communities surrounding their bunkers before the NCR / E-USA contacted them.