A sign like that would invite trouble.
I don't like the sign concept that much either because like I said earlier, it reminds me of the divisive signs we saw in the 60's. Imagine some small town where someone sees the letter outside a place of business and the idea catches fire and everyone agrees to do it. Slippery slope that has us moving backwards not forwards.
Company policies often have built in declarations that state refusal to engage in certain activities. There have been times in my own business where I have had to come right out and say "I can't and won't do that," usually dealing with insurance fraud. The owner has the right to state their religious beliefs to the public, and because it is a free market (or used to be)...customers can pick up the yellow pages and call/go somewhere else.
This relieves the possibility for contention and dispute because it is already public knowledge where the owner stands, and one of the primary issues, which a number in this thread have agreed to is...the owner's rights.
As opposed to the customer's rights to force an owner into something that violates their principles.
There is a difference between stating one's beliefs and racism. Show me the religion that is openly racist (in it's doctrine) and I will show you a religion that does not prosper here in a America. The only place they would be in a population that is primarily that particular religion, and Islam is a good example. There would be a difference between a sign that says "I am a Christian, this is a Christian store, please respect that," and "We do not serve blacks, Jews, or Methodists."
In legal circles there are obvious conflicts that need no discussion. A lawyer, for example, is not expected to engage in criminal activity because it stands in contradiction to the System of Law. The same can be said for Christians, and it would be a strange thing to see a "Christian Adult Shop" or a "Christian Bar."
The bottom line is that each believer has to decide issues for themselves and each will be held accountable for their decisions. I do not see this as an issue that can be painted black or white, with one position available, because the issue entails too many variables that have to be examined such as the motivations on each side, for example. If I were a Baker I would have no objection to baking the cake, but I would hope I would use the opportunity to witness. The sign would be the first statement of witness to the prospective customer. Most would, I believe, find another store, perhaps taking offense at the statement, and those that wanted to push the issue would, I think, create the circumstances where I would have the opportunity for a more credible and direct witness, giving me the opportunity to be specific about what God says, not what I think.
I love a good debate, lol.
God bless.