Why do we all have to identify as feminists with a label. Can't I just be a strong independent woman in my own right?
Because that is actually being a feminist.
In a patriarcal society, women will NOT be allowed to be independent or strong. That's a role for men.
I think tneissue here is that you are associating feminist with extreme what I would call extreme feminism. Plus you probably don't even realise how some stuff is so biased against women (I know I do, when you have heard some stuff so many times, they end up looking normal. You don't even question it).
And you don't have to agree with EVERYTHING either, like every movements, not everyone defend exactely the same ideas.
If I was you, rather than dismiss everything with the same brush, I would listen, even to those first word problem or eternally offended people, and try and see things from their POV. You might well learn something, change your mind or actually decide that yes it was indeeed being offended for nothing. But at least, this will be a thought out decision rather than a 'oh these feminists, they are just always offended about anything and everything'