Yes. They are born solely of dogma. That's what makes them religious principles.When those "principles" exclude other Americans from public businesses, then hell yes!But the merchants are making that determination with homosexual couples only. Had the merchant sincere concerns about sin, why doesn't that merchant vet each and every customer? That merchant could imperil his soul by selling to other sinners without knowledge! His only concern is disrespecting the gay couple.The baker is not judging the customer unworthy. The baker is not committing a sin himself. A baker might bake a wedding cake for a teacher accused of molesting students and still refuse to deliver a cake to an underage orgy.
You see this as an issue of the merchant judging the customer where he is really judging himself and refusing to commit what that merchant considers a sin.
When the government redefines religion in its own image and decides what beliefs people should have then there is no separation of the church from the state. The state has seized control of religion and dictates what others should believe and what they should do in accordance with that belief.
The merchant is deciding not to commit a sin himself. That is knowingly and with deliberation commit a sin. For monetary gain.
Should people be required to act against their principles?
If those so-called "principles" were part and parcel, basic tenets of Christianity, you might have a point. But such so-called "principles" both fly in the face of the basic tenets and are born solely of dogma.