Examples that come to mind: statistical modelling (reduction to nonparametric models), protein folding (reduction to quantum chemistry), climate/weather prediction (reduction to fluid physics), human language translation (reduction to neural networks).

Reductionism is not that useful as a theory building tool, but reductionist approaches have a lot of practical value.

I am not sure in what sense folding simulations are reducable to quantum chemistry. There are interesting 'hybrid' approaches where some (limited) quantum calculations are done for a small part of the structure - usually the active site I suppose - and the rest is done using more standard molecular mechanics/molecular dynamics approaches.

Perhaps things have progressed a lot since I worked in protein bioinformatics. As far as I know, even extremely short simulations at the quantum level were not possible for systems with more than a few atoms.

If you're looking for insults, and declaring the whole conversation a "culture war" as soon as you think you found one, (a) you'll avoid plenty of assholes, but (b) in the end you will read whatever you want to read, not what the thoughtful people are actually writing.