I was a licensed psychotherapist back in the day and there were no state regulations per se about what you could say to a patient. We had an ethical standard that spelled out in detail how we should conduct our practice.
No ethical therapist would advise that a kid or adult commit suicide and if they did the recourse would be to sued for malpractice, and I am pretty sure the patient or family would win in court.
Conversion therapy was not a thing when I was in practice, but I did have gay patients.
If conversion therapy( which is ineffective and harmful to those who go through it ) was brought to my attention by one of my gay patients wanting to pursue it, my first impulse would not have been, yeah dude, go for it. My first impulse would have been to explore his motivation ( often wanting to no longer suffer the societal hardship ? ) and explore how he would imagine his life to be as a converted gay person within his new identity and society in general.
But if parents sent a kid to me wanting him to undergo conversion therapy, that would pose an ethical problem for me and I would probably advise the parents to seek another therapist.