Acceptance vs changing your belief system, that is a hard one. I am in a relationship with a man from another culture and religion so I completely understand what your going through.
Do you mind if I ask some more detailed questions, so I can get a clearer understanding. You say you feel by accepting him you feel you will be changing your own beliefs? May I ask how accepting his beliefs will change yours? And Do you mind if I ask what are your specific beliefs vs his? Does it regard religion, how a man should act in your culture (eg he works and you stay at home, what you expect of him as a future husband ect) ect ect, as in could you give me real examples about what you argue about.

I don’t know if this helps but I thought I will write a bit about what we have compromised on, so that maybe it will help you.

My fiancé is muslim from an Arab country and I have been brought up in Christian/ atheist family in a western country.
He has accepted I will not convert to Islam (honestly I don’t know what will happen but I’ve said no, so we can come up with solutions to when we have kids) or wear the burka but will wear the hijab when I visit his home country (out of respect to his family and culture) but will not wear either when I am in a western country.

He is still free to practice Islam and I am free to find myself, regarding religion. (I will have pressure from his family but in the Quaran he is allowed to marry a Jewish or Christian women who believes in god, which I do)
We have established our children will be muslim (A must for him) and that is fine with me. Culturally he is allowed more than one wife, we have established I morally will not accept that so we will have a written contract that states he can not marry more than one wife (it is his culture but he does not want more than one anyway).

Even in relationships that are not from different cultures, it is normal to want your partner to change a particular habit but the beauty of relationships is that you get the opportunity to understand yourself more and find out what is really important to you in life as well as what you can and what your not willing to compromise on.

I hope that helped some bit or at least made you feel not so alone, that there are others dealing with these issue’s to. Because it can be hard when you feel like your the only one in a cross cultural relationship. 🙂