Legal Question in Criminal Law in California

Highly Doubtful.

No, however I answer using a secondary source of information. A former colleague of mine was convicted of a sex charge and he told me that he could not practice in that field anymore. I am not answering this question with a reference to a regulation that I can cite that says that sex offenders cannot obtain a license to work as a MFT

Probably not; however, that depends on the regulatory agency for MFT Licensing - and they may have provision to allow an MFT license, after their board consideration of the timing and nature of your conviction. Talk to a administrative law attorney familiar with the MFT Board in California. If you contact me, I would be happy to call/write the Board and ask them for their guidelines and see if you can get a hearing or a waiver.