Americans have always accepted that some of their tax money may go to things that they believe may be immoral; funding Planned Parenthood for example. But that is not direct complicity.
Under the HHS mandate Obama is trying to force people to directly pay for things they find immoral. It's identical to forcing a Jewish Deli to sell pork sandwiches with the excuse that the proprietors don't have to pork themselves.
It is clear that Obama is a fan of the concept of the government as Leviathan which can force the people to do anything. Sadly that's not what America is all about.