The answer: If Camille Paglia can call herself a feminist, anyone can. There’s no credentialing committee. I’m sure people can become feminists by mail, without any actual study.
Second question: Of course, people have the right to question anyone’s credibility as a feminist. In fact, it’s a minor sport. I give women more benefit of the doubt, sort of like extra credit for experience in the field.
One complication is the different definitions of feminism. But this is more than a question of semantics. Because of the Kyle Paynes of the world, women should always have the right to question a man’s feminism. I’m not saying male feminists are suspect, but for our own safety, we have the right to ask questions whenever we have doubts.
Kyle Payne was a rape crisis advocate, women’s studies student, and resident advisor at his university. While “looking after” an unconscious drunk student in his care, he undid her shirt and took a photograph and video of her breast.This comes from Lauredhel, who has gathered other comments on him. The description above is what Payne has acknowledged in a plea agreement, in which assault charges were dropped. Payne also inspired various posts in the 61st Carnival of Feminists. There are a number of sites that discuss men and feminism in general. Some good ones, such as XY, can be found in this recent Twisty thread.
To answer the third question: Yeah, I think Payne is worse than some other guy who did the same crime because he makes it harder for women to trust male allies.
ETA a second time: A colleague didn't think I should mention a commenter by screen name and so, I have deleted that passage.