How do I deal with glued-on drywall?
I would spend the time to scrape it off. This will increase the contact area between the studs and the drywall, which in turn will give better stability. Stability is important because if there is any free play, the screws will move, and may eventually show through the paint.

There are various scrapers available in your local home improvement store, in the paints/brushes section. If adhesive proves hard to remove, use mineral spirits or any type of adhesive remover you can find. 

I also found that a reciprocating saw with a scraping attachment can be efficient.