Even Supreme Court justice Scalia said that allowing religion to trump non-discrimination laws would set a bad precedent. People would then be a law unto themselves, being able to decide which laws they did and didn’t want to follow. Chaos would ensue.
Fifty years ago, racists were forced by law to serve black customers when the Civil Rights Act was passed. The government can definitely *force* citizens to serve other citizens they personally don’t approve of when it benefits society as a whole.