The wine application database rates various Quicken releases under wine, with the ratings varying from garbage for some versions, to platinum for others. YMMV, but at least some Quicken versions run.
Codeweavers rates some Quicken releases under CrossOver Linux as bronze, some as silver, with the overall assessment as bronze (which indeed carries a lot of warnings).
So I'd say it's not that winehq and crossover say Quicken won't work - but rather that, depending on version, it may work.
I myself run Q2007 H&B under wine 1.1.38. The basics all work. I haven't tried the transaction and investment download functions, which I suspect could indeed be more problematic.