Most liberal believers I've encountered not only refuse to admit it exists, but get outraged that you even tried point it out.

"Dominance privilege" is what all these people are struggling to define, but they need to define it in narrow terms by situation for polemical reasons.

Groups establish norms. They develop procedures that are convenient to the majority. Get mixed up with a large group of vegans, and the first thing you find is that to bring something with meat to a potluck or even to a lunch gathering becomes laden with rules. Because you might taint their food inadvertently. In that setting they're dominant, they have the power in that setting, and the omnivore winds up having his behavior curtailed. Why, exactly, should they have things set up to inconvenience the majority in favor of the minority? They don't. And there's no suggestion that they felt bad about it.

I've been in other situations in which I either support the majority by my attitude, words, and eagerness to comply with their logistics or I've been frowned upon in word and deed. Because the majority usually find ways to make most things that they do be convenience and serve their interests. It's rare to find a majority that whole-heartedly serves the interests of a minority, unless that minority has a lot of power. This can be an omnivore among vegans or vice-versa, a Xian among atheists or vice-versa, a conservative among liberals or vice-versa, or even somebody who likes "fine arts" music around people who like rock/country/rap (or vice-versa) or a monolingual among polyglots. So after an interpreting conference at Georgetown in my undergrad days we hit up a restaurant in Georgetown and flipped between English/Spanish/French (and, for the one Portuguese speaker, Portuguese). The significant-other of one of the attendees had joined us, was monolingual, and had to be actively defended against the polyglot supremacists. We swim like fish in seas that we are comfortable in; I've personally never found any reason to find not being in the majority and not having the majority bend over backwards to constraint their convenience for me to be a cause for complaint. Often there are easy things to help, but in the end it's something like majority rules.

(And even with all this, I'm broad-brushing too much. For not all Xians find the "Xian privilege" noted here to be anything other than oppression. Easy enough to deconstruct this argument, but there's still some validity. It's just that the writer narrowed it down for polemical reasons by using mis-generalizations about an out-group.)

the family of a fallen soldier in Iraq or Afghanistan had to fight to get their religion's symbol added to his grave marker. They were Wiccan.