I’ve worked in a couple of such places, and the advice I’d give is to ask them what they actually need, rather than just dumping boxes of stuff off. Far too much of our time was spent having to sort through stuff, then dispose of a lot of unusable gear. Some of the most useful items are chains, cassettes/freewheels (in good condition obvs), tyres, stuff like grips, brake pads of various types, saddles. Consumables, basically. Because these are invariably scarce (in any decent state at least) and need to be bought in, which saps resources even further.
As for ‘BSOs’; even some of the cheapest bikes can be made serviceable, as they are simple and basic. Full suspension BSOs should just be taken to the nearest recycling centre; we refused anything like that, unless it had other serviceable parts. But things like Shimano Tourney 5-6 speed mechs and shifters are absolute staples in being able to get basic bikes up and running. Posh stuff like XT etc, we sold on Ebay to raise funds for consumables.
Please think about ‘donating’ carefully; don’t just dump off your old shit on someone who lacks the resources to deal with it all.