I find myself continuously explaining to people how much of a benefit youth sports can be (soccer referee here) and how playing with your peers can be a really good form of mental growth and stability, and denying that to individuals because their outward appearance doesn't match their gender causes irreparable harm during a child's most formative years.

The chance that someone loses a scholarship to a trans child is infinitesimally small and the harm that is being caused to trans children through exclusion is guaranteed. The "think of the children" argument only works when you don't include the trans child themselves in the equation. Otherwise the choice is simple.

reminds me of the man's prayer from the red green show

"I'm a man but I can change, if I have to, I guess"

Alternatively, nobody should be allowed to play sports.