Actually, women do have the right to equal pay. It's the law. You seem to prefer that everyone is free to discriminate, but I think you can probably understand why most women would not want to give up their right to equal pay.
It's not a straw man, since there are many Republicans supporting so-called "personhood" measures, which would outlaw hormonal birth control. Romney and Ryan have both voiced support for that idea.
Yes, of course abortion is not just a woman's right. But to me (and to many), a few cells do not deserve the rights of a fully formed human being, with a brain, a heart and so on. If I were a woman, I'd be offended by the GOP telling me what to do with my body.
I like your signature.