This is not a question of parental rights. This is not a question of religious freedom.
The science is plain - conversion therapy is deeply harmful and carries disproportionate risks. By definition, conversion therapy is rooted in invasive incitement to durable rejection of the self. This is a separate phenomenon from appeals to a child's conscience, moral system, and religious beliefs or the parents' or religious leaders' guidance regarding such.
I am an LGBTQ person. As a child I survived a religion-driven family and social environment that was deeply and openly hostile to my identity. I survived by hiding my identity from my family, teachers, doctors, etc until I was of legal age. Even then I was still nearly coerced into consenting to focused conversion therapy, but instead left the state. Had I not been of legal age I would certainly have been forced into such "therapy" against my will and been durably and unreasonably harmed.
As a child survivor of Christian fundamentalism I can attest that a ban on conversion therapy is indeed needed. Such a ban will serve to protect LGBTQ children from only the most severe formalized applications of anti-identity conversion methods, and offers neglible insult to religeous freedom and parental rights.