If you are not a feminist, you don't believe in the equality of the sexes, right?

I'm not sure, this feels a bit like when people complain about "anti-fascist" as a label because it makes them feel pressured to be anti-fascist or otherwise be seen as sympathetic to fascism ... my question is why is anti-fascism (or in this case, feminism) so hard to accept?

I guess feminism works precisely by getting us to think about sexism and whether we think that is acceptable or not - I don't think it's good to be sexist, and I think it's reasonable to feel ashamed about being sexist. Social shame and taboo seems appropriate in this case, no? Like the anti-fascist example, fascists should be ashamed and face taboo for their views.

Not that you're wrong, some people will double-down in the face of opposition, this is precisely why so many fundamentalist churches promote street preaching, it doesn't convert people (which is the reason given for the activity), but it is effective at solidifying the loyalty of the member, since on the street they experience significant opposition, which bolsters their in-group identity. It's like a cult dynamic.

So yeah, it's probably good for social shame to be introduced for sexism, fascism, racism, etc. - but it's not a complete victory, the shame can induce stronger loyalties to those movements for those who still hold the views despite their taboo status.