Hillary made the comment that Christians will have to give up some beliefs. They will be forced to go against them and it would just be easier if they'd stop believing certain things.
They must cater gay weddings or attend them as photographers or face heavy fines and likely losing their businesses. Muslims have denied service to gays without an ounce of criticism over it.
The left does not fear Christians no matter how terrible they treat them while they understand fully that even a minor offense against Muslims ends in bloodshed.
1) When did she say Christians have to give up on some beliefs? Please provide a quote. (Please note that this is in no way a defense of Clinton. I just like sources when talking about this stuff in earnest).
2) As for catering gay weddings, etc., I'm not aware of any legislation or pending legislation that results in fines for refusing to make cakes or take photos at gay weddings. Please provide evidence. As far as I know, there's public condemnation, sure. But that's a far cry from legislation, and it certainly doesn't entail anyone being forced to stop believing in anything. It just means their business will suffer, possibly to the point of failure, because customers are aware of the photographer/bakers' discriminatory beliefs, and will choose to buy elsewhere. If the resulting pressure is too much for someone to take, as far as their religious convictions vs. their business interests are concerned... well, that's their own personal dilemma to hash out.
3) Again, as far as Muslims go, there has been one - and only one- news piece, etc., that I'm aware of that tried to draw a parallel to Muslim establishments, but it's received virtually no attention in the press. So you'll get no argument from me there.