That's crazy! You can wash a duvet cover 100 times & there may still be a small residual stain. Who cares? - Doesn't make it insanitary. I'm sure all my duvet covers have small stains if you scrutinise hard enough.... Some have faded areas where I've scrubbed a stain out.
I suppose it depends on your market/pricing..... I'm bottom end, cheaper than hostel prices, so I can't afford to replace linens for small stains ... But they're clean & I add disinfectant to every wash so any stains are sanitary! Top end, high price? ... Maybe then you expect no stains...?
- BUT your guest is practicing EXTORTION; Threats of bad review if....... - goes against Airbnb extortion policy. Your guest should have inspected the linen on arrival & asked you to change it if not up to his/her standards. How do you know the guest didn't CAUSE the stain? I think you were wrong to give a full refund.... just encourages scammers. (It's well known on airbnb you can get a free trip by complaining about something extremely trivial.)
I looked at your listings - nice enough, good reviews. But ORDINARY residential accommodation, (nothing wrong with that) - NOT HOTELS! So guests should expect the kind of linen they'd get staying with a friend or relative.... - Not hotel standard linen!