People don't wear sports team lanyards because they are pretending to be athletes. It's about support. Delta sells lanyards to passengers and anyone else who wants to support their brand.

I don't care to wear Delta stuff but I don't bother too much about what other people hang around their neck. It's also funny that the same folks who want pilots at the WO to wear hats to look more like Delta get offended when they wear a Delta lanyard.