TBH i wouldn't, it's not the "done" thing and showing is very traditionalist...but having said that, at lower local level you may get away with it, most of the judges seem to be senile, blind or a mixture of both and you may get away with it, anything is possible i have seen big fluffy purple numnahs and kids in pink jackets at the top end of the line ups!!!!
I cant help you - sorry. Would like to say thou that if a hackamore is the best and most comfortable thing for a horse, why cant it be shown in one? Surely its all about the comfort of the horse.
You might not get placed, but go for it and good luck
Well, we did a local but quite "serious" show as it was being used by all and sundry as a warmup for the local county show 2 days later in a bitless bridle as the pony was recovering from 2 wolf teeth extractions at the time. We put her in the M&M ridden class and the judge pulled her up from down the bottom to 6th after their individual, as it transpired later because she was so perfectly behaved with a child on board in the bitless bridle. (Pony stumbled on uneven ground, child fell off in the rosette winners lap of honour, so I had to go in and rescue them and got chatting to the judge who absolutely raved about pony's beautiful manners etc etc.) Oh and this was a "proper" judge who is widely respected in the area.
They also did family pony in it, we had to ask the judge's permission to enter first, explaining why she was bitless as the rule was to be ridden in a snaffle bridle. That was fine, they went and won that one!
Not exactly a hackamore I know, but she would have been wearing a hackamore if I hadn't known someone with a leather Dr Cooks bitless bridle that I could borrow.