A10 (rest of Temple sports) didn't have football.
Good point on Miami, but they stayed independent. I think the rule is you can't play in another conference that has your other sports.
If such a rule exists, it is not universal, but rather applies on a league-by-league basis.
Because here are some examples that violate this "rule":
1) Notre Dame ice hockey in the Big Ten;
2) UConn women's lacrosse and field hockey in the Big East;
3) Villanova football in the Colonial;
4) Temple women's lacrosse and field hockey in the Big East;
5) Cincinnati women's lacrosse and field hockey in the Big East;
6) Florida women's lacrosse in the Big East;
7) Vanderbilt women's lacrosse in the Big East;
8) Kentucky men's soccer in Conference USA;
9) South Carolina men's soccer in Conference USA;
10) West Virginia men's soccer in the MAC;
11) New Mexico men's soccer in Conference USA;
12) Denver men's lacrosse in the Big East;
13) Old Dominion field hockey in the Big East;
14) Air Force men's lacrosse in Atlantic Sun;
15) Air Force men's wrestling in the Big Twelve;
16) Tennessee women's rowing in the Big Twelve;
17) Alabama women's rowing in the Big Twelve;
18) Boise State wrestling in the Pac-12;
19) San Diego State soccer in the Pac-12;
In other words, if the leagues in question all allowed it, a team could play Big Twelve football, ACC basketball, Big Ten ice hockey, Big East lacrosse, Pac Ten volleyball, SEC baseball, CUSA soccer, and Ivy League gymnastics.