do you support any abortion restrictions?

[Okay, maybe Mike Johnson is a competent parliamentarian.]

Yes, some, based on things like viability and likelihood of fetal pain. I don't, on principle--although see below--support either special restrictions or special allowances based on the motivation for procuring the abortion, both because it's difficult to the point of pointlessness to really tell for sure why people do a whole host of things and because I don't think it's morally relevant anyway.

I'm familiar with the violinist thought experiment and don't find it especially convincing, in part because--and I understand that this is probably an uncommon position--I actually do think that one would have at least some kind of moral responsibility to the violinist in that case (although that responsibility may not be an overwhelming or decisive moral duty).

I'd be willing to entertain arguments on pragmatic grounds that there aren't any abortion restrictions that help more than they hurt, or that special restrictions or allowances based on motivation do help more than they hurt, since pragmatic grounds on the ones on which I support the legality of abortion in the first place.

[Okay, maybe Mike Johnson is a competent parliamentarian.]

Allowing abortion in cases of rape and incest sends the message to men that they can use women however they want sexually without consequence.  It essentially is the ultimate objectification of women. 

That...makes no sense at all.

[Okay, maybe Mike Johnson is a competent parliamentarian.]

Yes.  I am prolife and oppose abortion except to save the mother's life.  Allowing abortion in cases of rape and incest sends the message to men that they can use women however they want sexually without consequence.  It essentially is the ultimate objectification of women. 

How is making a woman have her rapist's baby a punishment for the rapist and not the woman?

It's not a punishment for either one.  It making sure that the rapist bears responsibility for impregnating the woman he raped.  If the woman can simply get an abortion, then it absolves the rapist for any responsibility toward abusing the woman and conceiving that child.  Since many rapes go unreported, it's quite possible that the rapist may not even face any legal responsibility for it.  If the rapist didn't want to impregnate the woman, then he shouldn't have raped the woman in the first place.  (He shouldn't have anyway, but that's beyond the scope of this discussion.)

The best way to solve this problem is to solve the problem of many rapes going unreported, not to ambiguously and extralegally punish everybody involved and the victim more severely.