Wrt the position of our enemy, anti-Islamists ARE "anti-Muslim," even if they claim to be Muslim. Our enemy's success depends on Islamism being accepted as mandatory and monolithic within their own cultural context at least (although such acceptance in the liberal West also helps them immensely). Again, why you would want to ENDORSE the truth of this key, and false, claim is something I can't understand.
BTW, Sakharov consistently focused his dissidence on issues of nuclear arms reduction, opposition to ballistic missile defense and human rights. He never openly denounced communism to my knowledge. It's not clear (at least to me) that he ever was specifically "anti-communist". It's enough that he was a dissident to the Soviet system.
Or should we not have supported his crusade unless he came out against communism specifically? Of course not. He hurt our enemy and confound his aims in any legitimate way that we can. We don't require dissidents to conform to some abstruse formula. It's enough that they dissent, in whatever fashion.