Sure, you could do a whole complicated testing system.
Or your reg form could have check boxes which accurately account for the range of how people see themselves.
We are talking about parents and kids, not master criminals.
o.k., let's give you the benefit of the doubt (something you didn't do for others very much during COVID debates) and say you've rethought your proposal but just can't bring yourself to say it. No more witchhunt, don't care about the y chromosome, not going to do a complicated testing regime...out the window. The new proposal is: clubs ask people to check a box...I doubt you are asking them "what gender do you see your child"....correct me if I'm wrong, please, but you are asking them "what sex was your child assigned at birth?"
It's a more streamlined elegant proposal, so let's weigh, measure and see if it's found wanting:
1. You've once again targeted MTF trans because you are singling them out with no express reason. Presumably let's assume it's not that you don't like them, or don't want them to play with your child, but you think they have a performance advantage. The issue here is you are neglecting the people who cheat (testosterone/steroids) and picking on the ones that just want to live their lives for a whole host of complicated reasons. So let's fix it for you: presumably the form has a box that asks you to confirm no steroid/testosterone usage. You also get rid of your FTM issue that way. Good so far?
2. Your premise is based though on the fact that there isn't cheating in the system and that people wouldn't lie. It's a false assumption. We know there are fake birth forms floating around out there. Let's fix it for you: yeah but we don't care enough to hunt down those people so we won't hunt down the trans. Well the other issue is that unlike the cheater, the mtf have the revised birth certificate to back them up.
3. The reality is in California your system doesn't survive legal scrutiny assuming that the parent has a revised birth certificate. It's probably discriminatory per se in the absence of a testosterone testing regime and the way the question is asked. A question which talks about testosterone levels might be able to survive the legal scrutiny. Now, you can argue that shouldn't be the ruling, but it is the reality. (you could also probably just rely on the birth certificate deferring the legalities to the state of California though you never know)
4. You also have the problem of well what if someone does want to challenge. Some coach playing for the state cup championship sees a kid and says that kid is trans...this is unfair....I want to challenge...might even file a lawsuit for a rules violation. Well, the issue there is you get back to testosterone...you going to allow challenges picking on the trans kid, you have to allow challenges for testosterone usage. So you've backdoored yourself into an (albeit limited) testosterone testing regime.
So, better, but I don't think you can ask the question that way and it sucks in the entire testing mechanism. Hence my thumbnail, if it's not important enough to steroid test, it's not important enough to worry about the trans kids. If you wanted to do a testosterone testing regime, it wouldn't necessarily extend to the whole system: you could cut out the younger ages, lower levels, non high level games...but to survive scrutiny it has to meticulously be tied to performance, not status.