I'd like to talk a bit more about the cheapest and most common process here. They state that ethyl acetate is below the FDA limits and therefore safe. For a start ethyl acetate is still pretty bad but it's not the cheapest.
Don't drink decaf. The CO2 method is pretty safe but the simple fact is unless you're sure how your beans were decaffinated you're better off not drinking it.
Another common solvent not mentioned here is Dichloromethane. It's a pretty clear cancer causing agent https://www.reddit.com/r/todayilearned/comments/pr8k9v/til_s...
You know what else is a solvent for decaffeinating coffee? Benzene. https://en.wikipedia.org/wiki/Benzene#Health_effects
Don't drink decaf. The CO2 method is pretty safe but the simple fact is unless you're sure how your beans were decaffinated you're better off not drinking it.