No, that is not what s/he is saying.
There is not a blanket refusal of services to "Christians," "Atheists" or what ever other classification we can come up with.
What is being discusses is a very narrow good/service to something that some people find distasteful. In this case, some Christians find the act of gay marriage distasteful, so they would prefer not to take part in one. But, they would be more than happy to sell to them in 99.9% of other circumstances.