I believe this is a bug, The guild in Monster Parts Hunt is asking for Spider Milk, but Male spiders drop Cum, while female spiders say there's no harvestable fluids.

I haven't cleared the tower yet, so I suppose there could be another type of enemy besides giant spiders I see.

It's correct that spiders don't have milk. They're arachnids. Rina no longer issues quests for impossible items as of version 24-3-18.