I've just had a really odd situation develop with my xH, where I was sending them without a bag but I asked him to return anything that needed washing. I then realised that he was asking the kids to strip at the door, change into 'his' clothes and strip half an hour before coming back to my house, back into the clothes they arrived in. Very upsetting for the kids and just weird of him to be honest - I can't understand why he would see that as a solution rather than just sending back washing... Sorry I've just realised this is a bit of a waffly response to your question and slightly off topic - apologies for long winded reply!
Anyway, our set up now, is that I've gritted my teeth calmly suggested that if he would like the clothes he has bought kept track of and returned that's no problem. I'll simply label the clothes the kids keep at my house in black permanent pen, and he can label 'his' in red. If a 'red' item turns up at mine, I'll return it, washed at their next visit. They can wear it in the time between visits too, if they want to. He doesn't have to hang onto any of the stuff they come in if he doesn't want to, as I'm happy to have it returned unwashed, on the day.
It's a bloody minefield but I think the important thing is how the kids feel. If they really like something, personally I think it's theirs, not mine or their dads, so they can take it, wear it, use it as they wish. I know that not every NRP is as weird about it as my ex, and not every RP is as ok with washing as me though, so I can't say whether labelling is a simple solution or not. I've yet to see whether xH will actually bother either labelling or returning anything... but the idea of the kids not being allowed to wear their own stuff, just because of washing/who bought it makes me sad.