Good hikers live by the “Leave No Trace” principle. Leaving trash of any kind on trail or thrown into nature is just awful to look at, spoils the beauty for others, and can endanger wildlife. This includes cores and peels from fruit, shells from nuts, and yes the toilet paper you brought. There doesn’t need to be a debate about what is the half-life of a banana peel, if you brought it into nature just bring a big ziplock bag and pack it all out. This includes picking up your dog's poo, bagging it and carrying it out. If you don't, the trail will begin to smell so bad, the dogs won't even want to hike there!
Another one to understand is vandalism. Vandalizing trails by defacing or destroying signs, markers, blazes or cairns can put lives in danger. Carving trees, painting stones (or bringing painted stones to leave) is just wrong. The need to express yourself or make a statement should end at the point it ruins the beauty of nature for someone else. You may think it is only a small painted stone on a summit or cairn of rocks you make on trail, but where is the line? Does it end at 1000 painted rocks cluttering the beauty of nature or maybe the decorative cairn you put on trail that ends up sending a hiker in the wrong direction? A good hiker leaves nature alone.
Pass this on and teach it to others.