If a person is sensitive to coffee or has gastritis, coffee can increase mucus in the stomach, but I could not find any study finding it increases mucus in the lungs. Coffee also includes polyphenols that relax the airways, helping us clear more mucus from the lungs,

I think possibly that opinion (caffeine can increase mucus) comes from people with "normal" lungs who may cough up mucus after their airways relax.

So, what we see as a benefit - inducing mucus clearance - others may see as an undesirable side effect.