I think in general that might have a kernel of truth but I don't see it much on CB. Seems like there's enough interaction on CB with LDS and non-LDS BYU fans that when I clicked on the OP to read it I expected to see a long list of respondents.
The irony with your statement that I quoted is, I think it is more commonly held by Ute fans whether LDS or not. I read comments on message boards all the time on this when it gets mentioned in some article online that BYU has a national fanbase. ute fans hate reading this and will frequently dry that it's only members of the LDS church that are BYU fans and that they don't have non-LDS fans that follow them.
As for the use of the word "members" or "non-members" I'm sorry if that seems high brow, I'm sure it's not intended that way. Kind of like if someone asks me if I"m a Costco member and I tell them no but I"m a Sam's Club member is how I see it. I don't perceive anything intended one way or another that Costco is better.
FWIW, I like the diversity of posters on CB. I like that there are some pretty decent Ute fans that will venture on here and offer differing opinions. I like that not all BYU fans were cut out with cookie cutters and that there are LDS, non-LDS, Utah based, living outside Utah (I live in Alaska), fans who attended BYU and those that didn't, etc. I think it makes the CB experience more enjoyable. I hope when things are all boiled down that others feel that too.