Sounds good but it's really just a form of tyranny that denies freedom of belief to those you disagree with, because there is no way to have freedom of opinion if you are forbidden to act on it.
When you hold public office, you are duty bound to to act impartially. No one is saying she isn't free to hold her beliefs or even the right to protest. But in the end the only solution is that she either complies or she finds employment elsewhere. I hold public office and there is plenty of policies and laws that I find disagreeable... But my feelings on the matter are irrelevant to the performance of my duties.
And you know, people would probably respect her a lot more if she simply resigned because they conflicted with her core moral beliefs. Instead she demands that the system kowtow to her.
The solution it seems to me is to avoid situations where there is sure to be a clash. Don't ask a Christian bakery to design a wedding cake for a gay marriage and so on. Have some Danish and coffee and order your cake elsewhere.
You cannot lump the two together because one is public office and the other is a private enterprise. You're absolutely right about the baker reserving the right to refuse service, but Davis is a government employee.
Edited by Hyroglyphx, : No reason given.
"Reason obeys itself; and ignorance submits to whatever is dictated to it" -- Thomas Paine