You can easily take them to any donation center. Nobody will ask questions because they will assume you're dropping them off for someone else and likely just don't care. If they ask questions then you can tell the truth or lie and say they are your sisters or friends clothes or something. Nobody will know the truth if you don't want them to.

If you want to get rid of bras and underwear keep them on separate bags from the rest when you arrive or before you go, ask if they will be accepted. If they can be, cool. If not I'm sure there's other places that will take them. Homeless shelters are always in need if there are any around you. They won't care as long as they are in hood repair and it would be best if they were cleaned. There are no shelters in my area so I have no idea what the requirements are since I don't have any to give to.