I think that as long as they provide at least BC beyond that is their choice. Like you said, it's a personal matter. And yes that does bring into play religious freedom, as a private company I think they are covered under that. That is an entirely separate debate though.
Maybe it's just me, but making the joke about trapping a guy by getting pregnant, and only mentioning STDs as a concern. Never saying that no you really shouldn't do that. I understand it was made in jest, but still.
Which is a valid point. We need to not be the same as feminists and overreact to a joke. Be the better people. That being said, it is still a sexist picture.