How do you carry your rifle or muzzleloader with you on you ATV? Looking for some simple solutions other than the gun boot type mounts as many of these do not look very sturdy to me.

I have tried different style holders and I can tell you the best solution I have found is to simply buy a cheap plastic, foam lined gun case and bungie it to your front rack.
For 20-30 bucks its cheaper than a boot, and keeps it completely protected from the elements as well as any mud or dirt kicked up by the wheels.
Been doing it this way for 3 years now and have no intention of changing anytime soon.

I just have the Y shaped holder on my ATV handlebars..they work great.But I haven't had any rain or mud holes yet either

I do like XTP...

I carry mine with the sling across the back of my neck with the rifle under my upper arms while I'm riding. I'm sure I'll take some heat on this, but I've been doing this for twenty five years, and had no problems, even when I fell off of a bridge with my four wheeler and ended up in a creek.