Being a theologian by trade and by belief, and an Army Chaplain of many, many years, I have see all manner of definitions of what people think of when they use the word “church”. Personally, I would consider the small gathering in the home to be a “church”.
You are probably thinking of a big building with parking lot and all kinds of programs.
In my opinion, it is incredibly unAmerican to impose laws that prevent residents of a neighborhood from building their own church building in their own neighborhood. Things such as schools, churches, stores, clubs, etc., MUST naturally be close to those they serve; that is, in residential communities.
When I lived in Tehachapi, CA, the local zoning laws doubled the cost of building a new worship center. They applied the same sort of rules used for supermarkets, and required parking and lighting beyond any plausible expectation. And they didn’t just require lights, but BRIGHT lights - high power, tall lights (expensive to install and run).
The new parking lot ended up costing as much as the new building!
I thought the church should have fought it, but I hadn’t lived there long - it may have been a fight would have led to more problems.
However, zoning exists and it is legal. Where I live, you can build an accessory building 4 feet from the property line. You can have a horse corral within 10 feet of a rear property line. But if you want to build a shade for the horses in the corral, it must be 50 feet from all property lines. Stupid, but I don’t have the money to fight it.
They have also been targeting horse arenas (riding areas) that were built under the old code, which required no permit and had no restrictions. They want to make the new restrictions retroactive, unless the owner can prove the existing structure was built prior to the code change.
I consider a lot of it harassment, and the county has admitted they want to clamp down on ‘rural’ uses...but the County is controlled by Tucson votes, and the Tucson voters only care about gimmees.
What I find so frustrating is govt bureaucrats thinking they should even have a say in the matter of people peacefully gathering at someones home. The govt gets away with this because most people can not afford to go to court and fight. Also, if you're dealing with local judges they aren't as independent as the federal judges and almost always side with the local govt because they need it's support.
The reasoning of worrying about a Bible study becoming a church could also apply to homeschoolers.
What if some homeschoolers got together in someone's home for a craft day every couple weeks? Would someone be pitching a fit about it maybe morphing into a school? It would make as much sense as worrying about a Bible study morphing into a church.
If the city feels that it can regulate Bible studies like that for whatever reason, there's nothing stopping them from regulating homeschools either because they aren't zoned as schools.