None of the tire shops near me care if you have Slime or anything else in your tires. However all of them in my area will charge extra to repair or replace any ATV or SxS tires, not because of sealant but because they are much harder to break and seat the bead on. Some shops near me won't touch them for that reason. I have six ATV's in my 'fleet' and have never been told to take my ATV tires elsewhere.
Story time: Back in the late 90's when I was a poor College Student trying to balance work, classes, truck payment, GF and ATV riding I rode a Honda ATC250R which had a rear tire which wouldn't hold air for more then a couple of days. I tried every sort of sealer I could find but it had old, worn-out beat-up tires which should have been replaced long before I actually got around to it. Eventually I found that a cocktail of Slime and Fix-A-Flat would keep the proper amount of air (less then 5PSI) in that tire and I forgot about it.
A few months later I scrapped together enough coin to get a new set of tires. On 'Date Night' I took my GF at the time to the local MC Dealer to buy and get my new tires mounted. The girl I was dating at the time was a gear head, the shop was slow and they didn't mind us walking around looking at the different bikes and ATV's they were working-on. As soon as they broke the bead on that ATV tire with the Slime/Fix-A-Flat cocktail in it, it blew Slime all over everything (and everyone) within 15' of the tire machine. The guy working the machine looked like he had come from a swamp, my GF had it in her long hair, it was a mess!
Needless to say no one was happy. I blamed it on the previous owner of ATV. They finished mounting my tires and suggested that next time I buy replacments someplace else. That also ended 'Date Night' as my GF wanted to go home and wash her hair. It took a long time before we could laugh about that one.
All that said I'm a big proponent of Slime. But I don't mix it with any other sort of tire sealants and I let the shop know what's in there. I also don't take my dates with me to get new tires mounted anymore