Above all, I am a Chinese student from mainland.
In my point of view, firstly,both 出于 and 基于 are correct. Then, which to choose，出于or基于，is based on sth . If it is abstract,such as mood,health,sympathy and so on,maybe you choose 出于 properly. If it is concrete,such as theory,fact,phenomenon,present situation and so on,maybe 基于 is better.
In fact, there is no clear difference between 出于and基于. They have overlapping range of application. As we Chinese students learning English, we are always puzzled in that which is correct in this sentence ,in or on? Maybe you English speakers would say,both them are correct,but in this situation,on is better,in that situation,in is better.
Moreover,as for what you mentioned,religion difference. According to my experience,Taiwanese is more traditional,using 基于 maybe more academic from their part. Maybe 出于 is informal.
By the way,出于 is widely used in spoken language and novel, unofficial report. 基于 is widely used in writing language,government report,thesis.
Hope these are useful for you^_^ enjoy Chinese