Oh I sympathise op.
FIL is obsessed with the bins. He always announces after dinner the night before "Bin Day tomorrow." He seems to take some degree of pride in making sure he is the most judicious in the county about what goes in his. No, that's food waste: it goes in the composting bin. No, that could go on the bonfire. No, that is recycling.
He seems to derive his self esteem from the fact his wheelie bin is the least filled. He honestly wheels it down the drive with one hand ostentatiously in his pocket, which I am sure is just in case anyone is looking to see how heavy (or light) his bin looks. The bins are his hobby.
Unfortunately his other hobby is the drains, and he seems to have plumbed his to choke and splutter on anything larger than a raisin. I was more or less instructed on my first visit never to introduce a tampon to his drains (he didn't actually use the word, but got there in a roundabout way by vetoing anything "like cotton wool" or "with string.")
Tampon disposal is therefore a major issue. I wouldn't dare put it in the bathroom bin as I guarantee he inspects them item by item as they are transferred to his wheelie bin.
I have ended up getting nappy bags and sometimes double bagging them, then smuggling them out in my handbag whenever we go out and finding a public bin, which seems slightly disgusting but there you are.
More recently I have discovered period pants actually work, but then again they can be awkward to rinse out and dry when staying as a guest.