Women can be misogynists. PoC can be racist and "reverse" racist. Atheists can be irrational, homosexuals can be transphobic, so on and so forth. Checking off one or more boxes in the minority checklist doesn't mean you are automatically understanding of all other minorities. Black preachers are some of the most outspoken homophobes, white cisgender homosexual men have been involved in transphobia and strangely biphobia (as in bisexuals). People claiming rationalism as their right by virtue of realizing there is no god make irrational judgements and racist and sexist and __ist remarks.
No one is immune to some level of stereotyping, it is part and parcel of our mental processes. But when it becomes an issue of actions, of social pressures, that is when you need to reevaluate. Never assume any group is immune. It may be one of my least favorite excuses of all time, when someone of a non privileged says something disparaging of another, or even their own grouping and then claims it is impossible for what they said to be ___ist. I hear women say "I'm a woman" as if to excuse their misogyny. I hear PoC claim to be immune to racism when they disparage another, separate race. It isn't even always about privilege, though it often is (white cisgender male homosexuals still have the first 3 going for them, so on). Institutional discrimination stays in place because the groups it hurts participate in it as much as the majority does. Rational evaluation is not just required of the privileged but by those hurt by privilege. Everyone should think clearly. Everyone should analyze and use logic and evidence to support their conclusions.
I usually just walk away from arguments that this comes up in. Relation to a topic is by no means a guarantee that you know anything about it.