Case law requires a doctor to continue to provide care for a reasonable period of time (usually one month is considered "reasonable") while the patient finds another physician. Otherwise, in most circumstances a doctor can drop a patient for any reason or no reason at all just as the patient can drop the doctor. I don't have a problem with that.
As a doctor, I consider gun safety a part of good medical care but it's not necessary to ask the patient intrusive questions about their personal lives. For example, I don't ask if they keep toxic chemicals in the home; I say, "If you have any potentially dangerous chemicals like drain cleaner, bleach, etc., it's important that those are kept out of the reach of children and preferably locked. Similarly, guns, knives, power tools and other mechanical devices that could cause harm should be stored securely away from children." There's no reason to ask if they have any of those things; my only concern is that if they have any of them, they have thought about the potential danger and secured them accordingly. I also don't ask if they ride motorcycles, ride horses, climb mountains, or bicycle; I just explain that when pursuing those sorts of activities the smart course of action is to wear a helmet.
I understand why the Florida law became necessary but I am ambivalent about it because I generally oppose the creeping destruction of the private and personal aspect of the physician-patient relationship. It also concerns me whenever another restraint is placed upon a private business. Just another reason to never practice in Florida.