The point you're missing is that it is not "far from a small percentage". It really is not.
And I'm not denying small percents of people cannot cause a huge impact. You are constantly representing an outlier to be representative of a whole group.
It's like if I took a tribal, homophobic group of a religion out of millions of people and made every member of that same religion out to be a horrible person.
The problem is that you can take all the negative examples you want, but they get in the news because they are negative, extreme, and vocal.
I'm repeating myself a lot, but you really only hinge on this one point, so...
It's not like the extremists of a group don't have their roots in the rest of the group.
Militant feminists simply take the flaws of feminism and exaggerate them, putting them before the more legitimate points.
The issue here is that the flaws were still existent in the base group, but just weren't exhibited so noticeably.
Islam for example, does indeed have it's
passages in the Qu'ran which promote violence to outsiders. But more moderate adherents to the religion simply 'interpret' them less harshly and do not put priority on them.
I'd dare go so far to say, yes, Islam is flawed as a whole. (Along with most other religions.) The majority might not believe in the worse parts, but that does not mean they are no longer a part of it. The only true solution is to completely scrap the beliefs system / group and start all over again.
Examples:
Feminism + MRAs -> Egalitarianism
Islam + Christianity + Judaism -> Atheism
Traditional Racism + Affirmative Action -> Equality in hiring with actions to equalize infrastructure and opportunities for the poor
etc.