I’m Treasurer for a Friends of the Library Foundation.
We gladly accept donations for free. They get sorted, and about 4 times a year we have a big booksale at the library. to sell off these donated items, plus books removed from circulation. The profits fund a bunch of programs & speakers at the library.
But there are restrictions on DVD’s (& CDs, VHS cassettes, LPs, etc.) – they have to be in an original box, sleeve, or container – otherwise they might be pirate copies. And these are for sale to individuals, not to add to the library collection. I believe there are copyright restrictions preventing library circulation of regular copies – they have to pay big bucks for circulating copies. That’s probably why they can’t accept your copies for their collection.
We do have restrictions on what we accept, but they are based on acceptable condition or likelihood to sell. For example, we don’t take encyclopedias, older diet or exercise or self-help books (those are all fads – anything older than 2 years is out of style & won’t sell), textbooks, etc. [Actually, we accept them, and then toss them in recycling. Refusing them discourages people from future donations. And many people just can’t throw away a book they enjoyed reading & re-reading, even if it’s falling apart. So they donate it, and we recycle it for them.]
We gladly accept political books – they sell. Either to a supporter, or we say to an opponent “come on, it’s only $2 – you’d have that much fun burning it at your next event” – and they buy it!
And we’re a lot less prudish than the OP about porn or near-porn. We get a fair amount (classic porn: Marquis de Sade, Kama Sutra, 1950’s marriage manuals, plus modern stuff), and it sells. We just put a sticker “Adult only” on the cover, and keep it far from the children’s section. Sometimes we’ve covered over front cover illustrations if needed. But anything that sells is more money for us to use in supporting library programs.