Not exactly the same issue but here in Bloomington, the locals wanted to have a vendor removed from our farmers market because allegedly, they have ties to a white supremacy group.
The mayor said that it is a public market and according to the First Amendment, they can't forbid them from coming and selling their produce.
It has caused a huge issue which is still going on and has basically killed the market. There was a lot of talk about taking the market private so they could oust the vendor.
So, wouldn't the same apply to firearms restrictions?
It sounds like the 2 situatons are structured differently. In Carmel, the Farmers Market is a private entity that basically leases the area that the market is on.
In Bloomington, it sounds like it is public space that is just allowed to be used for a market. Maybe a first-come-first-served basis? That would mean different rules apply.