I am a user, screen name reluctantone. I was banned during a private show. I was having a conversation about my depression and some thoughts and I was banned. I did not know this was forbidden conversation. We have been friends for many years, it was an innocent mistake. They banned my other accounts as well. Do you think that Chaturbate might show some mercy. I am a good customer and always conduct myself with integrity. 
Please advise.

You will need to contact support via their form on the support section of the site to find out why your account was banned.

Chaturbate have got to be very careful over certain subjects. Only they can remove a ban, but if an account has been terminated unfortunately they will not remove this & any new accounts will also be banned / terminated.