The idea that only girls should play girls in kiddie soccer is the actual nonsense concept. Otherwise you would be able to show us all that chapter in your biology textbook that contains the kiddie soccer "laws of the game". In reality, your point of view appears to based on the section of the bible that says you can stone trans children to death, but you obviously don't want to come out and say it.
Fundamentally, the entire concept of separating out biological men from women in sport has nothing to do with any "biology" either. If anything, "biology" supports just getting rid of gendered sports completely since everyone who plays is human with two feet and the ability to play the same sport regardless of gender. Who may and may not play in a particular sporting event is a determination made by those in charge of the event/league/association about what the decision makers deem appropriate and important, and what they do not. In the end, you have decided that trying to prop up your daughter's and/or your frail self-esteem is more important to you than the welfare and safety of a group that you clearly hold in contempt. But the youth soccer organizations that have you losing sleep have decided that winning and losing is not important compared to inclusion and ensuring that trans girls have as a safe place to play sport.
In the end, it is your fault your little princess isn't emotionally stable enough to handle the theoretical possibility that she might lose a soccer game because a trans girl was on the other team. You're the one who taught her to hate trans girls, but thankfully a youth soccer league has taken steps to help show her that trans girls aren't scary like her daddy has been claiming.