De Selby, clergy sex abuse and church-provided contraceptives are two completely different issues, and any attempt to link them for the purposes of discussing this issue is fallacious.
As for a Saudi company buying a US company, nobody is buying the church. I don't know why you made that part of your hypothetical. Nevertheless, the company would be absolutely within its rights to require women to wear burqas. The federal government might have a different opinion, though, although when it comes to Muslims, there's no guarantees.