I take plaquenil for rheumatoid arthritis (I was actually diagnosed with sjogrens first, it's complicated!) and I've found I can take it with my morning coffee if there is half and half in the coffee. In fact on my prescription it says take with food or a glass of milk. I think having even just a bit of fat in your stomach (so not skim milk) is enough to avoid any problems.
Taking it with food definitely does not make it less effective.