Surely you are now arguing against your own point? If one holds a wedding at a church, it is typically not open to the public any more than a wedding in a park. "Wedding crashers" aside, you invite people you know and it is typically not expected nor desired for the general public to attend. It's nothing unusual; churches schedule time for weddings all the time, and then go right back to being a public gathering space once the event is over. I should add, since it's part of the core of this debate, that the idea that churches are universally welcoming or truly public is itself debatable: they hold a religious function and while churches are usually open to all attendees, you will struggle to find community there unless you share the religious beliefs of the other attendees. That is to say, the church as a structure is open to all; the church as a community is not.

For what it's worth, my wedding was intentionally kept small, which allowed us to hold a ceremony without a permit and without closing off any public areas.