I'm not a fan of calling some schools half a school, based only on my own decision, especially since a fan in Georgia might well consider Georgia Southern a legit team but never have thought about Utah State as even playing football.

As far as all FBS schools per population, Utah is #7 with 1 FBS program for every 1.08M

The top 11 are (those with * have higher populations than Utah)
1. Wyoming 1:582k
2. W Virginia 1:892k
3. *Louisiana 1:929k
4. *Alabama 1:984k
5. Mississippi 1:989k
6. New Mexico 1:1.05M
7. Utah 1:1.08M
8. Oklahoma 1:1.33M
9. Hawaii 1:1.41M
10. Kansas 1:1.46M
11. Ohio 1:1.46M

If we only include "major" schools (unfortunately considered by most of college football landscape to be P5) Utah is still #14, despite being represented only by University of Utah.

Top 15 is
1. Kansas 1:1.46M
2. Mississippi 1:1.48M
3. Iowa 1:1.58M
4. W Virginia 1:1.78M
5. Nebraska 1:1.94M
6. *Oklahoma 1:1.99M
7. *Oregon 1:2.12M
8. *Kentucky 1:2.24M
9. *Indiana 1:2.25M
10. *Alabama 1:2.46M
11. *South Carolina 1:2.61M
12. *North Carolina 1:2.65M
13. Arkansas 1:3.03M
14. Utah 1:3.25M
15. *Tennessee 1:3.44M

If BYU is considered a P5, then Utah moves up to #3 at 1:1.62M, just behind Mississippi.

Overall, the states that really stand out to me as being very heavily invested in football (based on both number of programs, relevance of programs and population size) are
Mississippi (2 P5 + Southern Miss with population of 2.97M)
Alabama (2 P5 + UAB, Troy, S Alabama with population of 4.92M)
Utah (Utah, BYU, Utah State with population of 3.25M)
Oklahoma (2 P5 + Tulsa with population of 3.98M)
North Carolina (4 P5 + Charlotte, East Carolina, App State, with population of 10.6M)
Indiana (3 P5 + Ball State with population of 6.75M)