As a guy with oily skin, I’ve found adding a pea sized drop of liquid Dawn dish soap works well for this.

I have a similar problem with certain shirts in the armpit region, so here's my €0,02:

• Soaking said shirts in vinegar for a few hours before washing may help. It is said that that prevents black clotthes from bleaching as well, so that's two advantages.
• UV light seems to help. In other words: on a sunny day, hang your clothes outside to dry, inside out.
• I have a biological detergent that specifically targets protein and fat based stains like blood, grease, et cetera. Soaking clothes in a solution with that stuff works best for me. However, I do not know whether that stuff is for sale outside the Netherlands.

Any type of grease that stays gets washed in hot. Add .25-.5 cups of baking soda in the drum, front or top loader. And do a second rinse if your machine has that setting. Set the wash cycle to heavy. This works well for everything except knits like t-shirts & sweat pants. It will clean those but knits seem to hold that grease longer.

Try citric acid in the softener rinse. Will rinse out any leftover detergent.

Is it possible heat or moisture from you back is melting /dissolving something out of the been of the chair? Try draping a towel over the back of the chair while using it for a while to see if it intercepts this substance... Or maybe a sheet of plastic.

Could be a bad washer leaking oil into the wash. Had this happen in an apartment block with shared laundry. One machine did this, the other didn’t.

you could try borax powder, which mitigates hard water.

Sounds like the washer just needs to be cleaned. It's not water it's just old detergent. Go get some of the washer cleaning pods, home Depot has them, they're pretty much everywhere. Run a clean cycle, then another one after that just to rinse it, everything will be fine.

Get a water softener? Or use extra soap, or add some oxiclean to the tub

Maybe also try to use the vinegar in the wash cycle by putting it in the cup meant for bleach. Soaking it maybe isn't letting the vinegar do all it can do.

I listened to a podcast recently where they were trying to figure out a similarly difficult to remove stain someone was getting in the armpits of some of their t-shirts, but never on their sweaty gym clothes.

Bacne?