Not sure about college sports.
I don't know about community colleges but the NCAA, which covers inter-university competition at over 1,100 schools, doesn't allow transwomen to compete in women's sports.
Generally, when people talk about college scholarships for sports, the mean the NCAA.
NCAA women's sports:
A student-athlete assigned male at birth may not compete for an NCAA women's team.
A student-athlete assigned male at birth may practice on an NCAA women's team and receive all other benefits applicable to student-athletes. Division I leadership is planning to adopt roster limits in place of scholarship limits and new practice squad policies are still in development. [NB: The NCAA allows women's teams to have male practise players. They practise with the women's team but do not compete in inter-university competitions. It's fairly common for some sports like women's basketball and volleyball to practise against a few men along with the women on their team.]
A student-athlete assigned female at birth who has begun hormone therapy (e.g., testosterone) may not compete on a women's team. If such competition occurs, the team will be subject to NCAA mixed-team legislation, and the team will no longer be eligible for NCAA women's championships.
A student-athlete assigned female at birth who has begun hormone therapy (e.g., testosterone) may continue practicing with a women's team and receive all other benefits applicable to student-athletes.
Individual schools have the autonomy to determine athletics participation on their campuses.
https://www.ncaa.org/news/2025/2/6/media-center-ncaa-announces-transgender-student-athlete-participation-policy-change.aspx
I assume that the last sentence applies to intramural sports and sports not covered by the NCAA. E.g., some unis have men's rugby but it's not an NCAA sport. (Women's rugby is an NCAA Emerging Sport so, if the uni elects to have a team governed by the NCAA, it can offer scholarships and must comply with NCAA rules. Some men's rugby teams compete under the NAIA, see below.) Club sports are not governed by the NCAA or the NAIA.
The National Association of Intercollegiate Athletics, the governing body for mostly small colleges, announced a policy ... that essentially bans transgender athletes from women's sports.
The NAIA's Council of Presidents approved the policy in a 20-0 vote Monday, according to CBS Sports. The NAIA, which oversees some 83,000 athletes at schools across the country, is believed to be the first college sports organization to take such a step.
According to the transgender participation policy, all athletes may participate in NAIA-sponsored male sports but only athletes whose biological sex is female and have not begun hormone therapy will be allowed participate in women's sports.
A student who has begun hormone therapy may participate in activities such as workouts, practices and team activities, but not in interscholastic competition.
https://www.pbs.org/newshour/nation/new-naia-policy-prevents-transgender-women-from-competing-in-womens-college-sports