How do I stop my neighbors from leaving trash on their doorstep?

Well it sounds like the Direct approach would be the best way to go. Although, I'm sure most of these people are just too lazy to take it out regularly. I definitely would not advise the Pive Approach. Because if you started taking out their trash, in the hopes of them getting the hint, more likely they'll see an opportunity and allow you to take it out, even become dependent on you, worsening the dilemma. That's just way too much trash to take out. Since I don't like to confront people, I would personally just keep complaining to the management. Eventually they'll have to crack down on them, especially if animals are going through it. Well those are my thoughts, good luck.