I do wish that "oppositional sexism" was a more commonly known term. It was coined as part of transmisogyny theory, and is defined as the belief that men and women, are distinct, non-overlapping categories that do not share any traits. If gender was a venn diagram, people who believe in oppositional sexism think that "men" and "women" are separate circles that never touch.

The reason I think that it's a useful term is that it helps a lot with articulating exactly why a lot of transphobic people will call a cis man a girl for wearing nail polish, then turn around and call a trans woman a man. Both of those are enforcement of man and woman as non-overlapping social categories. It's also a huge part of homophobia, with many homophobes considering gay people to no longer really belong to their gender because they aren't performing it to their satisfaction.

It's a large part of the reason behind arguments that men and women can't understand each other or be friends, and/or that either men or women are monoliths. If men and women have nothing in common at all, it would be difficult for them to understand each other, and if all men are alike or all women are alike, then it makes sense to treat them all the same. Enforcing this rift is particularly miserable for women and men in close relationships with each other, but is often continued on the basis that "If I'm not a real man/woman, they won't love me anymore."

One common "progressive" form of oppositional sexism is an idea often put as the "divine feminine", that women are special in a way that men will never understand. It's meant to uplift women, but does so in ways that reinforce the idea that men and women are fundamentally different in ways that can never be reconciled or transcended. There's a reason this rhetoric is hugely popular among both tradwifes and radical feminists. It argues that there is something about women that men will never have or know, which is appealing when you are trying to define womanhood in a way that means no man is or ever has been a part of it.

You'll notice that nonbinary people are sharply excluded from the definition. This doesn't mean it doesn't apply to them, it means that oppositional sexism doesn't believe nonbinary people of any kind exist. It's especially rough on multigender people who are both men and women, because the whole idea of it is that men and women are two circles that don't overlap. The idea of them overlapping in one person is fundamentally rejected.

I think it's a very useful term for talking about a lot of the problems that a lot of queer people face when it comes to trying to carve out a place for ourselves in a society that views any deviation from rigid, binary categories as a failure to perform them correctly.