This isn't a matter of them paying for it... just that they are trying to select coverage that would deny paying for things. I am willing to bet that any of these companies objecting to it are doing it on political grounds, not religious.
No, it's all about religious grounds. This isn't as big of a deal with other companies, but Hobby Lobby is against the morning after pill and has chosen to offer insurance that doesn't cover it. Which they had
the freedom to do.
Obamacare wants to force them to offer insurance that covers it, which goes against their religious beliefs.
If a woman wants morning after pills to be covered so badly, she doesn't have to sign up for Hobby Lobby's insurance, she can get her own insurance.