I thought that if people had a trait that was usually privileged, they were just supposed to endure any mistreatment they received for it.

That's not actually a standard norm -- one thing worth noting is that when you look at the recent history of online SJ, what you're seeing is the proliferation of terms, tactics, ideas and theoretical frameworks from the last century, in a variety of contexts, suddenly become very visible and popular. Lots of people are discovering it, and in many cases what took decades or longer to develop in some groups is being adopted wholesale by people who are often familiar with summaries, or a few key texts.

A lot of people are finding it very empowering. Those people are not especially more likely to have deep insight, uncommon empathy, or a very broad view of the world than anyone else. This means they're going to be doing all the things people do in addition to talk about SJ, when talking about SJ.

Yes, this does mean some will be bullies, and sometimes whole groups will endorse that, essentially because in the process of bullying the person is also saying stuff they agree with, that they find empowering, and that is widely deprecated in society in general (often in ways that cause them tangible harm).

The trick is that bully-detection can run afoul of a related, but not similarly-pathological phenomenon. I wanna unpack this a little more because it's kind of complicated, and how well you see or agree that there's a distinction is often dependent on your own social values. It goes like this:

Some people have set up spaces to discuss some element of their experience in a SJ context -- say, a blog that deals with racism in popular culture, posted online. While technically anyone can access it if they know the URL, the blog is not written so as to be maximally-understandable to the widest cross-section of possible audiences. This is fine -- this is no different than discussing biology or astronomy publicly despite the sheer number of people who'd feel it was controversial to assert certain facts about evolution or cosmology, or who just don't know much about the topic.

People who aren't very knowledgeable about the topic, or have issues with it being discussed as a factual matter at all, may discover the blog and the discussion going on there. When they do, they'll often attempt to participate in the discussion from their own starting point, and when the immediate responses don't satisfy them, they'll keep pushing at it.

Thing is, it is really, emphatically not up to the bloggers or the commentators to bring them up to speed. It just isn't -- yes, education is important, yes communicating your point persuasively to outsiders is an important skill, but we don't expect the journal Nature to give everybody a basic, elementary-level understanding of physics before talking about the latest interesting results out of $LABORATORY. There's nothing especially wrong with pointing that out; doing so confrontationally might not seem very polite, but politeness may not actually be warranted either, as it'll merely encourage the person to keep demanding time and attention the folks there want for doing what it was they got together to do in the first place.

Explaining that this is not the place to come to be educated, or that it's not something they're volunteering to do, is seldom easy or productive to do gently. The goal is to get the person to stop trying to participate in a discussion they're derailing. Social and communication norms will play a big part in how that's phrased, too. It may be anything from arm's-length polite to trollish depending on the community and the individual involved. The common factor is that the purpose of communication on this topic is to end the discussion, which is consuming scarce resources of time, attention and energy.