I don't normally have a problem with that - I've been raised with mutt doggies - but they all came from a friend or relative.
If you have children though - getting a mutt or even a pure breed dog from a shelter could be a problem. Could - in if you do not know the history of the dog - you may not know what you are getting and I'd rather not have such an issue with kids.
Even one mutt we adopted from a family when I was a child, my parents ending up giving up from our family - he was too "snippy" biting at us kids frequently.
Reason we ended up going to a family breeder for us - we wanted the type of dog to fit our family and lifestyle. If I did not have children, I'd probably visited a shelter - where I have adopted all my kitties from.