Sparkly - // I strongly suspect that when the cake order was refused, the baker was bullied for his reasons. The gay agenda is quite clear. //
And I strongly suspect that you are looking for a scenario that did not exist in order to shoehorn in your belief that the couple involved in the case are bullies, and reactionaries based on their need to confront homophobia everywhere they find it.
If you are refused service in a shop, and the owner has advised you that he does not wish to give a reason for that refusal, do you seriously think he is immediately going to cave in and confess his prejudice simply because the customer asks him why?
Or, as in your scenario, the customer 'bullies' him into a response?
I think that hardly likely.
The shop owner can refuse, and politely decline to give a reason.
If the customer argues or 'bullies' him, the owner can ask the customer to leave the shop, and call the police if he refuses.