If that was a requirement for a private hospital, yes I would. I would disagree with it, I wouldn't go to that hospital but I respect private property and the right of the owner of that private property to operate their business (as long as it's not illegal) as they see fit.
I'm not saying that what Target did was necessarily illegal, I'm saying it was wrong. And I'm saying that for that reason, pro-life consumers should hold them responsible
And in a free market, that is a fully acceptable practice. However this woman does not have a court case
No physician should be required to perform an abortion, and no pharmacist should be required to dispense abortificents. If enough refused on professional, ethical, and moral grounds, Roe v. Wade would largely be a dead letter even if SCOTUS never overturned it.
At a minimum, abortion--even if legal--should not be easy to get. There should be moral, ethical, and professional hurdles in the way.