Baking the cake never was the question. It was inscribing it to the occasion — a 1st Amendment freedom issue.
I read where at least one of the bakeries gladly served them as customers for regular stuff. As you say - it was the inscription (and purpose) of the cake.
That whole “civil rights” thing sure had a lot of unintended (?) consequences. Obviously I can see that government has to be blind to color, religion, etc.
But if some business in the south wants to keep half (or more) of the customers in their area out of the store, that should be their worry.