So there is already at least one large conference that lacks divisions and uses protected matchups for football: the Big Sky Conference. There will be 14 football schools in the Big Sky in the 2018 and 2019 seasons (technically 13, as UND is FCS independent but is still playing a Big Sky schedule). Each team has 2 protected rivals, as shown here.

Right now they're using an 8-game conference schedule, but they may be moving to 9 games in 2020. That year North Dakota football joins the MVFC, leaving 13 football schools once again. Presumably, if the conference sticks with 2 protected matchups, MSU and UNC (UND's partners) will just play each other.

Since Idaho is rejoining as a football school this year, EWU is losing its protected matchup with UM. This could be reversed in 2020 by increasing the number of protected matchups. This also would allow Idaho to play ISU every year. Having 3 protected matchups in a 13-team conference means that one team is perpetually going to end up with 2 or 4 protected matchups, so perhaps 4 matchups across the board would be better.

Here's my proposal for the protected matchups for 2020 on:

Cal Poly: Sac State, UC Davis + NAU, SUU
EWU: Idaho, PSU + Montana, MSU
Idaho: EWU, Montana + ISU, PSU
ISU: Weber + Idaho, Montana, MSU (- PSU)
Montana: Idaho, MSU + EWU, ISU
MSU: Montana + EWU, ISU, UNC, (- UND)
NAU: SUU, UNC + Cal Poly, UC Davis
PSU: EWU + Idaho, Sac State, UC Davis (- ISU)
Sac State: Cal Poly, UC Davis + PSU, Weber
SUU: NAU, Weber + Cal Poly, UNC
UC Davis: Cal Poly, Sac State + NAU, PSU
UNC: NAU + MSU, SUU, Weber (- UND)
Weber: ISU, SUU + Sac State, UNC

With an 8-game schedule, each team can play half the 8 non-protected opponents every year. A 9-game schedule is doable; it just makes these pairings more frequent. Note that a 9-game conference schedule with 13 teams means one team will end up with 8 or 10 conference games. The team affected by this can be rotated annually.