What made it possible for at least some european christians of the renaissance era to embrace both the pagan aristotle and the islamic ibn rushd?

The reason why some European Christians were able to understand and embrace both Pagan and Islamic ideals during the Renaissance era was due to the increasing openness of tolerance and focusing on the moral values that are taught as opposed to the specific religion that is teaching them.

In my opinion, it was the renewed interest in antiquity and general secularist openmindedness, as opposing religious dogma and doctrine that had prevailed in the Middle Ages. In the Renaissance, intellectuals realized there was so much they didn't know. In particular, Ibn Rushd (widely known as Averroes) was an Islamic Aristotelian who was extremely committed to interpreting rationalist Aristotelian philosophy, thus transgressing religious and cultural boundaries, in a true proto-Renaissance fashion. That's why it was so easy for Europeans to accept him, while his own compatriots resented him.