Even though it may technically be someone's job, I still sort through my donations to make sure I'm not giving away anything in bad condition. I'm pretty sure no one wants to wear stained clothing - whether they're poor, needy, African, European or Asian - let alone have to sort through someone else's stains, lol! Erghh...
Back home, I would drop my donations at a high street charity store where I had a relationship with the owner (used to volunteer there) so I knew what sort of clothing they were looking for. Driving made it so much easier to do a big haul!
Anything outside of that MO was taken back home to Pakistan as hand-me-downs (the pushchair I used as a child is *still* being used over there now, after my own siblings - they don't make 'em like they used to lol!) Anything in worse condition, I'd cut into rags.
HK is weird in that, although charity shops do exist here, there isn't a big secondhand market due to cultural taboos around buying pre-owned (in particular, my MIL is worried we'll pick up something that may have belonged to someone now deceased). Sooo I sadly could no longer use old clothes as rags whilst living there - she'd insist on buying a brand new teatowel for it instead...
As a result, secondhand shops here are either the hipster vintage variety (which I never donate to because I don't know what's 'in' lol) or Salvation Army (usually far away from me). So I instead use the recycling bins for various charities nearby to home (no car). Though I'd say they're more like giant skips than 'bins' - big enough for someone to crawl into! (Unfortunately some folk have actually done this in the past to keep warm...)
Sooo thankfully this means that the charities regularly sort through the donations they receive to avoid that from happening - you see them doing it right there, by the skips.
As for clothing in worse condition, I no longer live somewhere where moth holes etc are an issue, so I have not faced that issue yet - that said though, small holes are easy enough to darn. So I now have a local community where we will donate clothing to anyone who's new to HK & struggling (HK has very few official resources for refugees since the govt don't home any of them here permanently but also don't allow them to work... as you can imagine, money is tight!)