Everyone that enjoys these mountains is different. Different religions, different skin colors, different political beliefs, different ways of life are all welcome in the mountains. Respect those around you, have patience, and be nice. Save the banter for the politicians.
The people you interact with most during your visit are the frontline workers that do their best to ensure every person's trip memorable and enjoyable. During busy months, frontline workers have to deal with a lot of travelers and are pushed to full bandwidth. Be kind to them, remember they are human too and don't rude to your waiter/waitress, bartender, cashier or tour guide.
Throughout the day, visitors can be in a hurry to get to the mountains, to their activity or to dinner. Don't be in a rush! You're on mountain time, anyway. Relax, drive with the flow of traffic and watch the road. Don't be be the angry driver on the road. Bikes and cars share the road in Durango. It's the law to give bikers 3 feet distance when they're on the road.
As cities continue to expand, we are expanding into a land that once belonged to animals. Respect them when you're in their space. Don't feed them, don't scare them, be quiet when they're around and don't leave your trash for them to get into. They will leave you alone if you mind your own business.
There are a few "rules" when being on the trail that can boil down to good trail etiquette. Uphill travelers have the right of way to downhill travelers. Allow those going uphill to continue their momentum by stepping to the uphill side and allowing them to pass. While hiking with a pup, remember to keep your dog on a leash on the trails designated to do so. Trails that can be occupied by different recreators also have trail etiquette. Mountain bikers are supposed to yield to hikers. However, mountain bikers tend to be moving swiftly downhill so it is in the hiker's best interest to stay alert. Mountain bikers and hikers yield to horses no matter the direction as horses are larger and can be spooked easily.