Another example of the government telling people how they can talk to other people.....
I have a problem with the 1st Amendment aspect of this too. However, I would be fine with such a bill if it applied only to patients whose bills are being paid in any part by public funds, and to doctors whose salaries are being paid by a publicly funded institution or agency, and to facilities which have been built and/or maintained with public funds (and that would end up catching a solid majority of pediatric offices). Taxpayers should not be forced to subsidize the medical profession's anti-gun political crusading (which is part of its larger pro-socialism political crusading). I suspect that in many pediatric practices, a very large percentage of patients are taxpayer-subsidized. Even worse, a lot of parents who are relying on taxpayer-funded health care programs for their children, are in programs where they don't haven't any choice as to what doctor they see, so the "if you don't like it, find another doctor" answer doesn't help.
When "talking to people" involves intimidation, conspiracy to deprive them of their Rights, and harassment under color of law; then the the government has a duty to get involved.