"no guys.... the bad feminists ARENT ACTUALLY FEMINISTS.... so dont worry about them! we're the real feminists! i believe the same thing as the bad feminists but please believe me! please!"
of course they're real feminists. if you say you're a feminist, regardless of your actual beliefs about what it means, you're a feminist. its just that most feminists don't share the beliefs that radical feminists do. the problem here is people like you aren't even involved in the feminist movement, so all your exposure to feminism is through /r/TiA and from other people. i'm a feminist, many of my friends are feminist, and we all share very moderate and egalitarian beliefs
my problem with people identifying as egalitarian is it's too broad
it's very easy to say "i just want everyone to have equal rights" but it's easy to have your own idea of where egalitarianism ends
i bet there are egalitarians who don't support trans people or feminism or mens rights or whatever
egalitarianism isn't conducive to activism either because it's too broad. you'd be more likely to find people who identify as feminists or civil rights activists or LGBT+ activists or whatever out and doing things. i suppose the exception would be the ACLU because they seem to act all across the board