From the article:
“The public debate began when an Ocala, Fla. pediatrician refused to offer care when a mother refused to answer questions about guns in the home.”
That doctor was an idiot, but it's not the government's role to tell idiot doctors what questions they may or may not ask, or which patients to see. If the doctor wants to ask certain questions and refuse to offer services to patients who refuse to answer those questions, the doctor should be free to ask the questions and refuse services to people who don't answer, just like a patient is free to refuse to see a doctor who asks the question. This "there oughta be a law" mentality is better suited to 'rats, not conservatives.