The APA strongly opposes conversion therapy (https://www.psychiatry.org/newsroom/news-releases/apa-reiterates-strong-opposition-to-conversion-therapy) "efforts to do so represent a significant risk of harm by subjecting individuals to forms of treatment which have not been scientifically validated and by undermining self-esteem when sexual orientation fails to change."

I respect the right of parents to parent, but this does not extend to the realm of harming one's child.

As a gay man that was offered the option of conversion therapy by my parents at the age of 17, I was also given to the option to say No.  I loathe to think of what my life would have been like had I instead said yes.  I can't imagine what my life would have been like if my parents had found out that I was gay at a younger age and had not given me the option because I was too young to make the choice myself.  I know other gay men and women whose parents loved them only on the condition of hiding/ignoring their sexual orientation.  I know other gay men and women who were not given the option by their parents, and were forced into conversion therapy, only for it to fail - they continue to this day to struggle with repairing the psychological and emotional damage that it caused them.

If you're a parent that supports conversion therapy, ask yourself why.  Is it really about helping your child, or is it really about addressing your own feelings towards different sexual orientations?