Co-ed is fine as an adjective to describe a school. It’s not fine as a noun to describe female students.
I would never have associated that sign with the kidnapping of students. I live in a town with more than one college, but I don’t think of it as a college town, though the businesses closest to colleges clearly are geared to the college crowd. I think it’s a mildly offensive joke, like many jokes it plays with stereotypes. I’m not a big fan of this whole trigger warning culture. “Warning! You might not want to read this bad joke!”
My favorite sign on a business was a travel agent whose sign said, “Please go away.” I chuckled every single time I passed it.