Arguably, the ability to rent your house is a constitutional one:
* https://fee.org/articles/private-property-and-government-und...
There seems to be a common misconception about zoning laws. Zoning laws fall under city planning where placement of certain types of buildings in organized locations leads to a more efficient city. These laws typically address traffic flow, utilities, etc.
So to forward the AirBnB context, the city zones an area as residential, a developer builds residences, and a private owner (again AirBnB context) purchases the property. From there I would contest that the city should have limited (if any) ability to limit or dictate how the now private owner choses to "use and dispose" of their personal property. Renting of the property does not violate the residential zoning...this would be as opposed to the owner tearing down their home to build an office sky scraper.
But if a private owner buys a house, they should be able to choose how to use that house. And again, this is off topic from the original thing I objected to: whether or not your neighbors should be able to dictate through government how you can/should use/dispose of your personal property.