If I come across an individual who doesn’t identify as their birth gender or any gender (so they ask to be referred to as they/them) what is the proper way to go about this? Do I still refer to them as he or she or do I call them based off of what they want? And how would I maintain the best mannerisms while navigating this?

You can call them “they/them”, particularly if not doing so can cause problems. However they are still considered their biological sex according to Islam and that is how you must interact with them