What criteria can we use to distinguish BYU either as a G5 or P5 since BYU doesn't belong to a conference at either level?
Some might argue BYU is a G5 simply because they claim BYU isn't P5. But if that is the basis of their argument then the exact opposite could be also true.
I'd suggest the following criteria to determine any schools G5 or P5 status.
A. Belonging to a G5 or P5 conference.
B. Having the same post season access as all other same level members
C. The status level of a majority of the team's regular season opponents
D. The school's overall health and longevity, meaning its budget, fan base, attendance, and tradition
E. The school's perception expressed by other NCAA members.

A and B cannot be used since BYU doesn't have a conference or a post season agreement aligned with P5's or G5's. BYU's bowl agreements are unique to the school and the bowl game has consisted of both G5 and P5 opponents. Using A or B criteria to show BYU is either G5 or P5 will be directly contradicted by using the same criteria.
C. I think this is a vital piece of criteria. This year BYU appears to be a G5. Next year BYU would be a P5. This will likely vary yearly.
D. BYU is clearly more similar to P5 status
E. BYU is a perceived P5 program based on direct official statements from other P5 conferences.
If you have other ideas for assessing any school's status level please chime in.