I've been on Rebif for almost 5 years. I drink socially and haven't had any problems. No doctor has ever suggested that I abstain.
I read that you are trying to decide between Rebif and Copaxone. I selected Rebif in part because of the somewhat flexible treatment schedule. Some weeks I do MWF, others MThSa, TThSa, MWSa, etc. I just make sure that I get 3 doses in per week and that I don't go more than 72 hours (or less than 48 hours) between doses.
I figured that if my liver enzymes elevated, I could switch to Copaxone. I DID have a short period of time during which my enzymes were elevated, but they fell back to normal range in a couple months. Apparently, that is not uncommon.
Good luck with picking a therapy,