Since you believe that people should refuse service to certain individuals then you should have no objection to not being served by someone.
If someone doest wa t my business I would happily push on
If I ask someone to perform a task that they replied is against their religious beliefs I would thank them, tell them I understood and meant no insult, and gracefully exit the establishment. Thats what should happen in a society that respects other peoples beliefs. Its odd that for a large city with apparently such a big demand for queer themed cakes the only place to get a cake is that particular baker, or perhaps there are other options but this baker is asked just for the purpose of trying to get him to bend to man’s law rather than God’s law.