My old mare had regular AQHA papers. The little guy has appendix papers and the plan was to show him and earn his full papers. But he didn’t turn out as expected. He obviously didn’t care one whit about my plans.
I’ve encountered breed bias in both directions. Moving forward a few decades, people seem to be more open minded as long as the horse can get the job done safely. (And many probably wouldn’t mind having a @TomNeese horse turn up in their barn. I sure wouldn’t!) IME off-breeds are more prevalent when owners are less competition focused and/or more DIYers. But others may have different experiences.