1. I don't think it undermines Rai's credibility at all.
2. There's a difference between linking yourself with something and having that link constantly shoved down your throat by people who bear you ill will.
3. I do not think that most Christians take the attitude that you do. I think they compartmentalize. I suspect you do as well, perhaps not knowingly. Do you feel that the African countries pursuing such barbaric anti-gay policies in the name of christ fairly represent Christianity?
4. I do not think that there are any Muslims anywhere who lack that comparable recognition. But how else to communicate to people who remain, by choice, wholly ignorant of Islam? I had a Muslim student who spent some time talking to various Christian groups at the law school. He stopped, he told me, because it became the same thing over and over; first question was "why do Muslims hate Jesus," and the answer given, "actually, we revere jesus" was never accepted and there were people willing to fight him over it. Ironic, given that he was a pretty chill guy being accused of a violent religion by people jumping at the chance to fight. But anyway, you can't talk to people, so you have to say, "they do not represent my views or the views of 99.9% of muslims worldwide"