Detergent doesn't actually strip the DWR.
You just aren't really supposed to do it as it clogs the pores in the membrane. However if you rinse well afterwards, or tech wash afterwards then its okay. If your gear is really filthy then tech wash doesn't clean that well, but detergent does.
No, it doesn't clog the pores in the membrane. What happens is that stuff like Persil and the like contains a whole bunch of chemical additives, things like optical brighteners and, particularly, wetting agents which help water to penetrate fabrics. The latter, in particular, are the last things you want on a waterproof jacket.
The residue from this stuff masks the DWR - Durable Water Repellant - finish on the fabric and stops it beading. The surface layer of fabric - face - then soaks up water. The material is still waterproof as that's down to the membrane layer, but because the outer layer is soaked, it's no longer breathable, so you get wet from condensation from your own sweat more rapidly.
Using a detergent - it doesn't matter if it's bio or non-bio, that's a myth - doesn't permanently trash your jacket, it just means you need to remove it for either the original DWR to work or to reproof it effectively. A couple of washes with a pure soap detergent - Nikwax, Grangers or similar - plus a double rinse should do that.
If the jacket's relatively new, try gentle heat-treating, either a careful iron avoiding reflective areas, following care instructions or, if the label permits, a low temperature tumble dryer session. That may be enough to revive the original finish and allow the face fabric to bead again.
If not, you need to re-treat it. The usual guideline is to use wash-in for single layer (actually 3-ply fabrics) and spray-on for two-layer fabrics which have a separate mesh liner. Neither Nikwax or Grangers need heat treating any more apart from the Grangers Two-in-One combined cleaner and proofer products, they work fine with just air-drying and Nikwax make a real point of this as they don't use fluo-chemicals which need heat to work.
Of course you can do all this and if you run hot, you will still get sweaty and the fabric will struggle to cope. If it's really wet, water will rub down your neck and you'll get wet that way. And even the factory DWR will lose effectiveness after a few hours...
Both the Grangers and Nikwax websites have comprehensive instructions and explanations etc...