Ah, but once you make it income property, you pay property tax at that rate whether you have tenants or not. I've seen plenty of Masonic centers with vacant office space, paying high property taxes. We explored getting full-time renters for part of our building, and it went nowhere. A couple of nibbles, but no renters. There are plenty of shiny new office buildings downtown that have space available.
I wasn't saying that lodges shouldn't do that, and I know that some are very successful. I was more responding to the idea of having some outside management group take care of the building and rent it to the lodge. That puts you in the "income property" category, even though nothing but the Masonic Lodge is housed in the building. If the Lodge owns the building, it's taxed at a fraternal organization rate. Your mileage may vary.