Most all my elk hunting in Wyo is under Gen tags. There are 2 outfitters that run out of the same trailhead that I typically hunt. One runs a backcountry camp and one runs day hunts on horseback from the trailhead. The one that runs day hunts is a great guy. Pleasant, considerate, he even packed half a bull out for me. The other one is a horses ass. The trailhead is small and he will take the entire turnout to get gear arranged and pack his horses. Guides for both groups have never been anything but kind, considerate hunters. Never had a problem with their hunters either. Most are surprised that people hunt where they are without horses.
One thing that has helped me when trying to figure out how to hunt the same drainages they are, on public land, and trying to be considerate of them as well is that in my experience horseback hunters rarely get off a horse trail. I use this to my advantage. Their general tactic seems to be to ride trails to lookouts, sit for awhile then move to the next one, then back to camp. I simply hunt the canyons, timber patches and slides that don't have horse trails running through them. I hunt areas that they ride right by. Doesn't even have to be far. One timber patch that will always hold elk is only 50 acres in size and 90 yds from the trail. I have found elk in that timber patch every time I hunt it. Another area that is a consistent elk producer for me is a slope that has a very popular main access FS road at the bottom and a horse trail on the ridgeline at the top. The horse trails come out of the trailhead, loop up the slope, hit the ridgeline, run along it for a few miles then loop back down the slope to the road. I hunt, on foot, the area inside that circle. I have been hunting that spot almost every year since 2001 and have taken 9 bulls and 5 cows from it in that time.
For the most part, when it comes to elk, I don't sweat outfitters or any other hunters for that matter. I simply go to where the other hunters aren't. Whether they are outfitted or not. Seems the elk do the same.