It's good you didn't send an 'I quit' text as it might, like you rightly said, backfire on you.

Talk with him. Is there no other way - apart from physical touch - for you to feel that you do matter to him for that one hour a week?

If he's a good T otherwise, please weight carefully between: losing him over his refusal to hug clients or staying with him knowing hugging would most likely not be forthcoming.