THEN ... it can be appealed on Constitutional grounds, if it is as you say ... and they will win (again, given that your stated understanding here is correct).
I am not as optimistic as you when you say that these bakers can win on constitutional grounds.
Judge Andrew Napolitano for instance ( not a left wing nut by any stretch of the imagination ) argued when interviewed on Fox News that the free exercise of religion is only limited to the exercise of religious ceremony and doesn’t include business, and on top of that, the government has no business doing things “based on hatred or stereotypes.”
Napolitano noted how, years ago, businesses could discriminate on the basis of nearly everything, from gender and religion to race and ethnicity (like those infamous “No Irish Need Apply” signs). He said that it’s one thing for a priest to be able to refuse to marry a gay couple, but if people are allowed to invoke religion to get a free pass outside of religious ceremony, the logical endpoint is someone saying “my religion prohibits me from paying taxes or obeying the speed limits.”
THAT my friends will be the basis for arguing that the fine against the Bakers is CONSTITUTIONAL.
(not that I agree with it ).