You may be right, but I suspect that whatever the reasons, you have to be ready to defend them.
Personally, I could care less who wants to get married as long as they are both adults.
I don't get how baking a cake or not has this much meaning for some people. If I were a baker, my goal would be to sell cakes not judge the folks who are buying them.
Let's take this to an abstract situation:
Would you supply the firewood to an execution where someone was burned alive?
I would not. If it were legal? OK, let the shareholders talk - why do no pharma companies supply the USA with sodium pentobarbitol for executions anymore? Money...
Yes, money talks, often louder than morality, but you can see how people may find something objectionable - when there are 1000 other businesses offering the same service (this is not an emergency medical procedure, it is a cake...why get so angry that one person won't make a cake for you?).
It would not bother me, or 95% of people, but why force the 5% who object to do something they feel is morally reprehensible? That is just bullying in my view.