People are just worried about welfare.
I no longer think this is really true. Mainly because the way people go about 'debating' the problems with cross breeds is in a manner least likely to actually effect any change at all.
If they cared about dog welfare, they would approach the subject differently because they would be more focussed on changing opnions than on ranting.
Proper debate, with the real pitfalls debated in a reasonable manner will have greater effect. Calling them 'mongrels' in a way intended to make someone think less about their dog will not.
(FWIW I happen to think mongrels are the very pinaccle of dog kind so it is no insult to me, but does seem to be used that way)
Cross breeds do come with extra challanges, because of their nature.
It's hard to find decent breeders who have chosen healthy parents, have higher welfare standards and understand the full spectrum of things they must provide to produce well rounded and healthy dogs. That means, as an owner, you are on the back foot already and should look to take even more care in researching and choosing your puppy.
Cross breeds tend to have a less stable genetic line than pedigrees - so you are taking a bigger gamble on the kind of dog you will end up with. You should be prepared for that and be clear on the very worst aspects of the contributing breeds - and be ready to handle that. If you have stricter/more narrow set of criteria for your dog then find an adult that already shows the right temperament or choose a puppy from a stable line - which, at the moment, tends to mean a pedigree.
F2 cross breeds can be less healthy than their parents - i.e. without proper genetic testing it is easy to breed faults back in again because the parents did not dispaly them. Bringing me to: there are much more health tests required to breed crosses than pedigrees so you need to find a breeder that understands that.
They are a puppy farms wet dream (the crosses chosen are often about litter size, not temperament) - and farmers are crafty as fuck. A first time/novice puppy buyer might do well to find someone more experienced whop can help them sort through the rubbish to find someone decent.
They are not more 'hypoallergenic' than a poodle. If that's a criteria then the more stable bet is for a full poodle (poodles are awesome dogs).
However, this horse has bolted. I really wish the KC would adopt the more common crosses so that they can be extended the (albeit limited) protection that provides and so that the liens can be stabalised to produce gerater consistency in temperament.
All that said, pedigree show breeders have - collectively and over generations - pretty much fucked a large number of breeds. So they do not get a free pass on this 