PJay, welcome to the forum. We have another recent member with PBC, so she should be able to help you with some of your questions.
A diet free from red meat is best for anyone with any type of liver disease. However, I don't think it's really necessary or particularly advantageous to eliminate all meat but fish. Skinless chicken breast should be okay. Ditto turkey. I make turkey burgers and really prefer them now to beef burgers (ground turkey is cheaper, too, but does need a lot of seasoning.) Once in a rare while (about once a month) I give in and have filet of beef or beef stew, but I always feel worse afterwards (headache, sluggish, just not well), which is enough to make me stick with my diet 99.9% of the time. So I would say it is okay to give in to your craving occasionally if it becomes too much...just don't make it a habit! I'm not a doctor, so this is just my own opinion and experience.