A Psychiatric Survivor movement exists for a reason. Thomas Szasz refers to the coercive psychiatry systems that exist as forming psychiatric slavery. He wrote a book entitled Psychiatric Slavery which explores a Supreme Court case related to psychiatry (Donaldson case, which has a Wikipedia article I believe).
The history of psychiatry is filled with torture and human rights abuses.
Suicide prohibitions deter people from being able to have open and honest conversations about suicide in private (like with a counselor).
I believe if we ever want to be able to have a real significant reduction in suicides we need to stop using psychiatric coercion, force, and confinement to prevent and deter then. We need to use large amounts of persuasion, reason, and kindness if we want a significant reduction of or elimination of suicides, which is indeed a worthwhile goal. Are suicide prohibitions are remnants of a Judeo-Christian quasi-Sharia law?
Should only atheists and agnostics be allowed to engage in suicide? No, all adults should have suicide respected as a civil and human right, when done in private.