I totally agree with your view of how the word feminism is now perceived and how that came to be, which was why I asked why you even want to be associated to it, when you can just call yourself (gender) egalitarian and people would understand you without all the added baggage.
As for existing sexism, it is more prevalent in some industries but not in others. In my personal experience in IT, I've never seen females treated less than males, but maybe that's owed to the sheer diversity of the people working there. That said, I've heard about it happening from people I know, and statistics about it shouldn't be hard to find online.
I do sort of agree with your view that assertiveness plays a factor, and also do think women are less assertive than men in general just from my experience, but that's also because they are playing into the gender expectations for them which are so ingrained into society and people's minds. That's actually one of the things legit feminists fight against, the antiquated perceptions of femininity, such as being modest and quiet.