“It’s a lot of one time visitors up here. They just aren’t thinking, they are on vacation mode. This is their home, we need to respect that.”
Unfortunately, over the years the goats have become habituated to human presence and show no fear, even walking right up to people but park officials warn there have been cases of goats attacking hikers in Colorado, especially when they have young around. The best thing you can do as a visitor is to give all wildlife a respectful amount of space and bring a zoom lens for your camera.