It's not really providing material support or facilitating a campaign, they are baking a cake.
Except they're not just baking a cake, they have no objection to baking a cake... They've been asked to bake one for a campaign group with a message in it - by not baking it they've not provided material support.
I don't think bakeries values should be on political campaigns but rather baking cakes and setting aside everything else.
It doesn't matter what products/messages you think someone else's business should and shouldn't cater to - it's up to the business owner. Whether that means they don't make green cakes because they don't like the colour green or they exercise discretion over the messages they're happy to print on cakes.
I don't think comparison with the photographer is comparable since clearly the baker offers the service to begin with aka writing messages and images, where as the photograph fro the onset doesn't offer the service. It would be comparable if the photographer didn't allow certain colourings to some peoples photos and on others.
The photographer clearly does post processing - he's simply refusing to do some forms of it that he dislikes artistically.
Up to this point no issue, its not my beliefs. Just like if I ran a printing service and a client asked me to print bibles. I'm not endorsing the bible or its teaching, I just print stuff.
So would you print BNP fliers? Or could you see that some people wouldn't want to print things they oppose?
That would be something a Muslim could not do by action, difference is that would be across the board rather than selective. It is not endorsing or facilitating, simply something they couldn't do irrespective of the client.
It's something they could do physically, they just wouldn't as a result if their beliefs... Why would that belief be OK but other personal beliefs not be an OK objection? You either have freedom of speech/expression or you don't... You can't elevate some beliefs/choices and decide they're more worthy of protection.
They believe gay marriage is wrong, not writing text for someone else's belief of gay marriage
No they quite clearly believe that that would be wrong too else we wouldn't have this issue in the first place. It might not be an officially endorsed religious position such as not drawing a prophet... but that isn't important - the important point is that they believe creating that product would be wrong... that is their belief whether you or anyone else likes it or not.