We had a record library where I was too. I joined for a year and taped most of the CDs I was interested in (this being 1989, not 1999) along with LPs and other cassettes. Didn't rejoin the next year as I had most of what I wanted...!
Still bought CDs at the time- doubt I'd have bought more if the library hadn't been around as they were bloody expensive and I couldn't afford more anyway! It's easy to forget how expensive CDs were back then (and remained so until the early 2000s).