Al-Jahiz (d. 868 CE) had an interesting approach to foreign cultures that I believe should be the modern Muslim’s approach as well (despite disagreeing with him on theology):
Jahiz was to advance the theory and practice of Adab1 by employing it as a system for the study of nature and society, a system that eschews narrow specialization in favour of a discursive, multi-faceted approach, willing to investigate all natural and social phenomena in a tolerant and sceptical spirit. Jahizian Adab is an Adab which believes in the infinitely didactic possibilities of nature, in man's need to investigate this world of reason and harmony which God has placed at his disposal and for his instruction, a world where even the 'wing of a mosquito' is enough for a lifetime of research. For Jahiz, Islam is, intellectually, a beginning and not an end. He believed that Islam had inherited world civilizations and that its true task was to carry through this legacy, to advance it by claiming as its own all the best that had ever been thought or accomplished. Just as Islam was the final and complete religious message, so its culture was to be heir to all earlier cultures. Accordingly, neither the veneration of antiquity or foreign cultures nor a conservative refusal to tolerate foreignness was acceptable but an open-mindedness which sought wisdom in all its manifestations, and whatever its sources.
Tariq Khalidi, Arabic Historical Thought in the Classical Period (1994)