If a private business doesn't want to make a cake for someone, that's their business. It does seem curious why such a nonstory is a story when the press doesn't seem at all interested in so much material that's out there about the man about to become the most powerful living person...but silly me, I forget that THIS kind of foolishness is REAL news these days.
You are correct the business should have every right to refuse to make any cake they do not want to.
Much like pharmacists should have every right to refuse to fill prescriptions they feel are against their religious beliefs.