The reason you don't get it is because it is totally dissociated from the issue at hand.
In the US churches get all sorts of privileges...most notably being untaxed no matter how much revenue they generate. They are also pretty much exempt from laws, including this one. There is equal protection under law, so the state (now every state) will issue a license to any couple who wants to get married. But a church, being a church, is allowed to say "we will only allow people of our faith to marry in our building." That's why, as someone else already noted, you won't see anyone marrying a protestant. No one has tried it, but the "church of god's people are all white" could open a lot of legal worm cans.
This is no more an attack on the tax exempt status of churches than it is an attack on their exemption from obeying the law. That is just the usual dog whistling. Any time anything happens that some of the religious fundies take offense to they immediately chant "What's next? Taxing the churches?" because absolutely nothing can create a unified front of outrage among religious leaders faster than a perceived threat to their money.
Thanks, I think this explains it. So it will (probably) not happen, it is just a good way of generating interest in the topic.