The content presented to the kids by Drag Queen Story Time in the UK seems to be somewhat different to what's being peddled in the USA by Drag Queen Story Hour, the American group that inspired the UK group.
From what I can gather, the UK group reads children's books that are pretty standard in any library, such as "The Very Hungry Caterpillar." The US group, by contrast, presents content that they provide themselves that specifically celebrates drag, transgenderism, gender fluidity & so on - and does so in a way that's supposed to foster tolerance but actually promotes misogyny & sex role stereotypes.
My guess is that the US group might've started out reading conventional children's books to the kids, but over time they began developing & bringing in their own material. Which is why tots in the US reading hours are being taught new lyrics to "The Wheels on the Bus" such as:
The hips on the drag queen go swish swish swish
The heels on the drag queen go click click click
The lips on the drag queen go smooch smooch smooch
Unfortunately, children's books promoting transgenderism - such as "I Am Jazz" (aimed at kids 4-8), "10,000 Dresses" (for kids 5-9) & "The Gender Fairy" (ages 4 & up) - & belief in an innate gender identity separate from biological sex that "only you can know" - like "Jacob's New Dress" (ages 4-8) - are now so commonplace in libraries that these groups can do their propagandizing by using materials from libraries' own collections.