How can they justify that friendship?
They are in a state of denial. The fact that their cultural imperatives include Regressive politics is at odds with the fact that Muslim scriptures call for the death of homosexuals:
Hadith: "Narrated by Abdullah ibn Abbas: The Prophet (peace be upon him) said: If you find anyone doing as Lot's people did, kill the one who does it, and the one to whom it is done."
(Sunan Abu Dawood, 38:4447)
"Narrated Abdullah ibn Abbas: If a man who is not married is seized committing sodomy, he will be stoned to death."
(Sunan of Abu-Dawood – Book 38 Hadith 4448)
And then to turn around and blame Christians is absurd. Jesus never called for the death of homosexuals.