From my experience I can only guess about the brush. The stiffer side would be able to cut through the hairs better, and get all the way through the beard to your skin beneath it. You would start with this one. The softer side would probably be for final styling.

I bet google knows the answer if you ask it.

Also - on the religious-based comments - if you're quick enough, you can usually turn these comments into compliments and teach the person a little lesson at the same time. "I'll take that as a compliment, I've seen lots of *insert religious group here* men with pretty awesome beards. Thank you."