I do not think that a museum needs to engage with pop culture in order to make itself interesting to museumgoers. Museums are already interesting and engaging with pop culture for its own sake is just a quick way to seem and become dated.
What would I put in a museum? Probably a museum! That's an amusing relic of our past.
I am amused by cricket because it seems to take longer than baseball and I like that. It seems like a sport I could have made up it - it takes several days to play and everyone wears sweaters. I can't confess to knowing what's going on at all.