Even dropping them on the ground first fails to work for a lot of people.

Did this with about 9 games, unable to change clothes at all, ended up glitching even carriers, helmets, backpacks too.

I have the same issue. I am unable to take clothes even from ground unless I have dropped them myself. I am able to change my head gear etc. though; only back packs, clothes and vests seem to be affected.

Could this be somehow related to http://feedback.arma3.com/view.php?id=1588
even though they say that picking clothes up from enemies is deliberately disabled?

No this is in General for All NATO clothing or Op4 clothing, Its the same, you need to drop it on the ground using the tabs at the top then pick it up.

Have had this problem with backpacks added to containers using addBackpackCargo as well.

Issue was looked into and fixed.

Thank you for reporting this issue to us. We appreciate it, keep up the good work and help comuinty and developers to build better game for all.

Should be fixed in 105634.