If he's not willing to accept your work then I would suggest breaking up with him rather than caving. Firstly, because you shouldn't date someone who looks down on you and secondly because it's a sign that he thinks he has the right to be controlling of his partners. This could just be the first of many times he thinks he can use the 'I'll break up with you if you don't do X' line.
If I date someone who does something that I consider a dealbreaker, I don't ask them to change that thing for me - I leave and find someone who is a better match. There are people out there that will respect you as you are. I've dated two sex workers in the past. One made very clear from the start that she enjoyed her work (she'd worked in retail for 10yrs previous and much preferred working for herself) and would not give it up, and I respected her decision.