I am going to try to say this in the nicest, gentlest way possible via the internet, talk to your bf about this.Despite my boyfriend's threat to wash my hair, I don't think it looks bad.
I say this because a one time bf suddenly went no soap or shampoo and it was a major reason we broke up. Bottom line, he stank. He had extreme dandruff. I tried to diplomatically talk to him about it. He said he did not. But...to me, he did. And, people I associated also with mentioned privately to me how he looked/smelled like a transient.
I totally totally understand going no soap or shampoo for health reasons and/or even to save money. Just to please be a little careful in your own society/culture/circle of peoples.
I am not saying YOUR bf is going to leave. I am NOT saying you stink. I AM saying this is a major change in lifestyle in the middle of an established relationship that may not be entirely okay with the other one.
So, please, talk about this with him even if his threatening is just a joke.
I apologize profusely if my post has offended anyone.