Las Vegas does not allow atheists to perform wedding ceremonies
Apparently in Las Vegas pretty much anyone can get a license to perform weddings -- Elvis impersonators, faux Liberaces, etc. -- except atheists. The rules are that in order to get a license you need to have ties to a congregation. The congregation can be as small as two people. But still, that's the rule. If you're not willing to lie and invent some kind of pseudo-religion that you're a member of, as atheist Michael Jacobson was unwilling to do, then you're barred from performing weddings.
Seems like a clear entanglement of church and state to me. Here in San Diego anyone is allowed to be registered to perform weddings for a day. No religious affiliation is required. So my sister was able to sign up as the "minister" and conduct the ceremony for me and my wife.