Feminists are feminists because, between the sexes, women are objectively the disadvantaged group. It may be worth adding here that, for me, feminism is not simply about rights, but about the realization of actual equality between men and women. "Rights feminism", if you will -- the kind that is mostly or entirely concerned with battles in the legal arena -- is alternatively known as
liberal feminism. I am a
radical feminist. The content of the general culture is important to me too.
Incidentally, who says that being a feminist precludes one from also being a populist? I regard myself as both.
A term can be pejorative or used in a belittling way without being a hate term. The term "right-winger" would be an obvious example because it's not even a slur. Most conservatives would indeed accept that their ideas are politically right-of-center and perhaps call themselves rightists. Consider last year's infamous "Unite the Right" rallies, for example, or the mere fact that there exists a movement calling
itself the "alt-right". Stuff like that. Many rightists, especially far-rightists, freely associate themselves with the term. In other words, to call someone "right wing" or a "right winger" isn't intrinsically an insult even, so it doesn't even count as a slur let alone a hate term. A hate term is one that is imposed on a distinct group from without, absent their consent, and frequently used to incite violence, threats, or advocate genocide, stuff of that nature; to create a toxic climate of terror.