Oh goodness. That is a difficult problem.
If they are disappearing from the laundry basket and that's in a public place like the bathroom. Then I would have a second small hamper in your room for personal use.
If they're disappearing from your room, perhaps start "nicely" with a notice inside your lingerie drawer / the hamper saying- "Please leave these alone and buy your own." That might be enough of a hint that they've been busted. That they'll be embarrassed enough to stop.
If that doesn't help, then consider a discreet camera. They can be very cheap [or a repurposed smartphone.] Or possibly try to borrow one, since you won't need to all that long. That way you at least know who to talk to. And I think honestly taking them to one side and saying "This is an expensive and unfair habit of yours. You need to stop it now, or you won't be welcome here any more" is fine. Technically it's theft and they would NOT want it reported to the police.
Finally, a motion sensor alarm on the drawer would also put paid to it. Although more publicly than any other route. And there'd be a danger of forgetting it was there, as you dressed in the morning, and scaring the daylights out of the household.
But I think any of these are better than having to hide your things or lock them up. I guess this doesn't help if items are disappearing while being laundered or drying.