Maybe it is. But I definitely think it shapes their positions on issues like this. Childhood, from an Evangelical standpoint, is a eternal war waged against the powers of darkness, and one that Satan is destined to essentially win. You cannot stand alone against His might. You cannot by your actions or teachings raise your child to be good. No one is good. The smallest thing could drag them off the path. You can only protect them long enough to be saved by magical means, by accepting baptism at the appropriate time and then sticking with it through adulthood. The fear isn't that any particular theater act will turn them into bad people; they're already bad people, who without God's guidance are fundamentally inclined to all manner of evil acts from cheating on taxes to bestial-clown-orgies to murder. The fear is that they will leave the church community and thus become endangered by "the world". If that proposition were rational, their response would be, because attending a drag show most certainly does challenge fidelity to this perversion they've made of the earthly church.
In other words, it's a Lovecraftian, not Campbellinian, reinterpretation of the faith. Encountering the world, crossing the limens of community safety, can only lead to darkness and madness. You don't want your kids meeting new people, or going on quests, or suggesting useful changes to the village management style. So a drag queen story hour cannot possibly be anything but a threat, as it did not originate from within the community. A double threat in fact - non-Christian books and gender freedom. Danger on every side and chaos beyond the gates.