There are many examples of these fights. Hikers don't like to hear motors. So don't hike on roads. Or close roads to motorized use to increase your enjoyment. Mountain bikers don't like equestrians - our MTB stoke thread turned into an anti-horse discourse for a bit, despite the obvious notion that horse property owners probably have the political clout to ensure trails are protected from development so that broke ass mountain bikers can complain about them.
Pfft! If anything, wealthy equestrians have used their political clout to keep trails closed from bike access. That's where the animosity comes from.
I thought the snowboard ban at Alta was stupid... until I actually skied there. There is some validity to the traversing argument. At Alpine Meadows we also have some very long, long traverses where stopping your momentum is a huge PITA. Most of the time it happens it's because a snowboarder is in the way scooting along (or sitting down) and it's extremely frustrating. Skiers can cause this problem too, but it's far less often.