There is still the occasional puff of smoke coming out from my ears over the media coverage of a state whose name I dare not mention. That and my experience with the Maryland Senate hearings on the Trans-Rights, aka "Bathroom Bill" which eventually passed. It is amazing the propaganda and fear mongering that goes on.
Deborah covered the obvious
1) All men are scum (direct quote from about every female friend)
2) All men want sex
3) Men will seize any advantage they can to get sex, or just to "get off"
4) 12 y/o girls are especially yummy
There are plenty of laws on the books covering perverts and rapist be they wearing a dress, or it taking place in a rest-room. The stats plainly demonstrate that up untill the immediate aftermath of the State whose name I dare not mention, in districts that had bathroom bills in effect no trans person was ever charged with a crime. You're 12 year old daughters are perfectly safe. Well, just as safe as they otherwise would be.
I don't get all the hoopla myself. In guy mode I've had several experiences of women needing to advantage themselves of the empty stall in the Mens. Nobody freaked out, not even the woman being in the den of potential rapist. Like Geeker said, we just want to do our business and leave, just like any other woman.
If "You've been asked...." I sort of suspect there have been rumblings from your coworkers to HR. How comfortable are you with doing this? Essentially, I think you are being asked to make a case as to why you should not have to use a dedicated toilet.
There may be sites like the Transgender Law Project or others similar to it that have some material they can use. There are also outfits that do this sort of anti-discrimination training for a living.