If a girl can run, pass, block, tackle as well or better than others on the team, I can think of no particular reason to exclude her from being on it — except for "Ew, girl cooties" and "Eek! How improper!"
Ohio Girl Fights Back Against Ban From Middle-School Football Team
Makhaela Jenkins was barred from joining her middle-school football team because she’s a girl, but now she’s challenging the district’s policy.
Like boxing, it's another of those sports whose participants have counter-intuitively suffered from "improvements" in safety equipment.
For smaller schools I can understand the logistical issue. My High School was so small that men's and women's events were scheduled off nights because opposing teams had to use the opposite sex locker room. Well a female football player makes this more complicated.
But there are solutions to that problem.