You don't have to let your friend go if she's that important to you in my opinion. But if you respect her and her religion while not having one yourself then I think the least you could do is trying to be a little considerate around her. Try not to curse, smoke or drink alcohol (which ARE wrong and not really needed in life if you ask me. But I don't think cutting your hair is) around her would be a good start I think. But most importantly, talk to her about how you feel and try to find a solution that will satisfy you both. Otherwise the uneasiness might become worse the longer you wait and it might even drive you apart when it's not really needed. But whatever happens, I hope that you both will find what will make you happy. Good luck.