Anti-feminist vs. Sexist

Correct me if I'm wrong, but I'm pretty sure "anti-feminist" isn't really a thing. In fact, I am fairly certain that the opposite of feminist is sexist. Anti-feminism is sexism.
Let's do some quick (and overgeneralized) definitions.
What is feminism?
Trick question. There are actually multiple types of feminisms. Emphasis on the S as the end. Fun fact, when you type feminisms you get the red squiggly line of death underneath it. I promise you though, it is a real word and concept. Feminisms vary by issue, but all are committed to the equity (you can say equality but that is some problematic language) of all genders/sexual orientations. Feminisms are more than just making women equal to men. Firstly, which men are we trying to be equal to? I'm assuming white, rich men because let's face it they have all the power. But are we really trying for power?
I digress.
Sexism is discrimination of a person/persons based on the sex/gender that the sexist person identifies s/he as. Homophobia discriminates based on a persons supposed sexual orientation.
I am aware that I am being really vague and round about with my wording. But that's because gender/sex identity is so much more complicated than man/woman. Same with sexual orientation. These are not things that can be put nicely into labeled boxes. They are more complex than that.
So, back to my point. What is an anti-feminist? Someone who is against feminism. Someone who is against gender equity (if not equity in general). This kind of sounds like a sexist. Ta-dah! They are the same thing!
Now, I really don't like the term anti-feminist. It's like you're trying to say "I'm not sexist but, I really think women should be heterosexual, pregnant, and in the kitchen" (being pregnant doesn't mean you're heterosexual). It also is just bad English. It's not a word. I don't care if you put anti in front of an existing word, if there is already a word for what you are trying to describe, just use it.
For example: Pinterest does not have anti-feminist undertones. It has sexist undertones. It actually has a fuck ton of sexist undertones. In fact, depending on which board or category you are browsing or even who you follow, it's just straight up sexist. But the same can be said of the world.
Put that in your juicebox and suck it.