Your analogy doesn't actually cover what the case is.  Your analogy seems to be focused on the decoration of the cake, rather than the fact that they are, in your words, "a Neo-Nazi, a KKK member, and a gay person".  If he denies it based upon the design of the cake, then there is no discrimination, as he wouldn't sell that cake to anybody.

However, let's take your last example: a same-sex wedding cake.  At the point that Mr. Phillips knew, there was no discussion of the design of the cake at play, so you can't say that it was going to be designed some way that would be offensive towards Mr. Phillips on the design of the cake itself.

Furthermore, what exactly differentiates a same-sex wedding cake from an opposite-sex wedding cake?  Can you tell a same-sex wedding cake just from looking at it?  I sure can't.