They're not legally wrong, they are just leaving me in a tough situation (try to find a new tenant over the holidays). 

I would never tell tenants what temperature to keep their home at, even if it was legal.

Ensure your attorney is well-versed in lending regulations and set up a strong legal framework.

This is definitely not the path I would take unless the numbers are sweet and STRs are fully legal in the zone your are buying.

In my case, it's totally not discriminating, it's only 1 legal bedroom, so only right for a single person or a couple. 

AshleyNormal, however you have wide latitude in the actual agreement you agree to sign, how long, how much commission, that’s not to see individual agents have to agree to your terms, but if you feel uncomfortable with the terms you are free to negotiate or shop around, however an agent cannot legally show you a house without an signed agreement of some sort. 

Legal options?

The linked article claims 8 out of every 100 renters are evicted annually, but that only counts tenants evicted through the legal system.

If something goes wrong with the property—like debts or legal issues—your personal stuff is generally safe.

Right now, this type of arrangement is perfectly legal (clinic within SFR neighborhood), but that could always change.