I have no problems with any cross whatsoever and, in fact, I prefer grade animals, in dogs at least. As for horses, it doesn't really bother me, but it does get annoying with all these new 'breeds' popping out of the woodwork every couple of years from just that much work, rather than the hundreds of years of specialized breeding that it took for every other breed. I'm fine with calling your dog a labradoodle because it's easier than saying lab cross poodle, or a multi****, cavoodle or chug. I'm fine with your horse being called a Starab (which s really the only one of those sorts of names I've ever heard in the horse world), but going so far as to register it as a breed... I'm sorry, but I don't think that has any purpose.
But, saying so, that disregards one of my favourite 'dream' horses, the Irish Sport Horse, since all it really is an Irish Draught x TB... Even so, IMHO I think that going so far as to register a cross without refining the breed down by breeding type to type is just an excuse for the purebred elitists to feel like they are owning a brilliant horse rather than 'just a cross'. Keep in mind that that is not my POV, I love crosses, but I've met many of such 'elitists' that think that way.