Of course it should matter. "Sorry but I can't make the cake you want today because we've run out of brown icing but can provide it in a couple of days time" is massively different to "Sorry but I refuse to make a cake that depicts ethnic minorities on it".
No the reasons for refusing to support a political stance shouldn't matter...
How is making a cake 'supporting a stance'? It's just fulfilling an order. Would the bakery turn down a cake that said "Liverpool Will Win The League This Year" if the owner thought it was unlikely, of course they wouldn't.
the same way that agreeing to print BNP leaflets supports a stance... if you're fundamentally opposed to the view then you'll likely want to disassociate yourself from it and not support it by helping to add to any campaign whether that be by refusing leaflets or refusing to bake a simple cake with a political message
But a newspaper can't refuse to take an advert if by doing so they are discriminating against a protected group.
they'd likely only be doing that if they refused to take an advert based on who the person requesting the advert was rather than based on the content of the advert... a newspaper should have complete freedom to refuse any content it simply doesn't agree with/that conflicts with its editorial stance etc... in the US this is protected by the 1st amendment...
likewise the baker is denying certain content - he's not denying a cake in general to any group... I'm sure the customer could drop the suit and go back and buy a cake..