From what I understand of drag, it is a style of expression akin to an art form or a theatrical performance. Just as any other art can be overtly sexual, drag can be too, but like movies, music, and sculpture it can be used to express a wide range of complex topics.

The mother reacting poorly to the story time is misinterpreting the concept of drag likely due to preconceived biases or social influence, and that interpretation should be corrected through exposure and conversation. Ideally they would seek that learning out, having recognized that the flyer made them uncomfortable. Maybe they go to the story time without their child and respectfully watch to see if such activities would be appropriate in their eyes for their child in the future.

The jack-ass competition sounds like a real legal liability for the library and city given the physical harm likely to be brought to participants, so I doubt it would be likely to exist. I also doubt many parents would sign their kids up for such a competition.

Assuming the flyer were there and approved to be there, it would not be an issue for the reason stated either. You can not and should not expect the world to hide your child from everything harmful, if they notice and ask about it, it can be a learning experience for them to talk about why they can't participate. It's also not the first time they have seen that sort of behavior, their classmates act like that on the playground and the cartoons they watch have it in every episode. Tom and Jerry or Bugs Bunny comes to mind.

Society isn't degrading, the arguers view of society is being challenged by reality. They can learn and adapt or learn and remain but either way the onus is on them to exist with society.