No, it doesn't have anything to do with minis and Shetlands competing against each other - that happens in AMHR classes with ASPC/AMHR animals all the time and has for as long as there has been an AMHR (dual registration is far from a new thing!)
The issue is that the same judges are judging BOTH breeds at the same show. Judges are human - they are going to remember a horse from an earlier class in the other breed. This isn't fair to the person exhibiting that horse (especially if the judge didn't like the horse, or it acted up, etc.). It isn't fair to the exhibitor that isn't showing a dual registered animal - he's going to have to be twice as good to get that judges eye when put up against an animal that had a spectacular showing earlier.
To me, this is no different than the fact that you cannot show in different ASPC divisions with the same horse at the same show. Say I have a Foundation Certified Modern that makes Foundation height. I could in theory show it in all FOUR Shetland divisions - it qualifies for all of them in pedigree and height. Let's say this is a great animal - tons of eye appeal, great ring presence, and I have the skill and it has the training to either rev up or go easy to show in all four divisions. Would it be fair to the other exhibitors for me to show that pony Modern and then turn around and show it again under the same judge in Modern Pleasure, again in Classic and again in Foundation? Heck No! Would it save me money at shows? Sure - but just because it would save me money doesn't make it fair.