By nature, mixed breeds are going to be more variable in their coat type, which absolutely can include how much they set off a person's allergies. There are very few of the popular poodle mixes who have been breed over several generations until they produce a consistent look (including coat type) and temperament, and by definition those are not F1B crosses, which are only two generations deep (produced when a 50/50 cross bred back to a purebred of one of the parent breeds). F1B also doesn't refer only to a litter where a 50/50 parent is bred to a pure poodle - it can also be that the 50/50 parent was bred back to the other breed in the mix (like Cavalier or golden retriever, for example).
So while it's true that the more poodle a mix like this has, the more likely it is to have a poodle-like coat, it's much harder to predict how an allergic person will react to that coat than with a purebred. And since each puppy inherits different genes from its parents, you can get pretty extreme differences within the same litter.
Another thing to consider is that, whether mixed or pure, a responsible breeder needs to be running genetic health tests on their breeding stock to avoid - or at least significantly reduce the risk of - producing puppies who have heritable illnesses or disorders. While some breeders of mixed breeds are doing this, it's much rarer than it should be, and without that testing you're really gambling over whether you're getting a puppy who could develop a serious medical problem that could have been avoided if the breeder was doing their due diligence. If you do go for a mixed breed, research the testing each breed should go through
Here is what the Poodle Club of America suggests testing all breeding poodles for, depending on size, at the very minimum:
Health Testing in Poodles. Mixing a poodle with another breed doesn't eliminate these genetic issues, especially when you're breeding back to more poodles. Pretty much all of these conditions exist in other breeds, so breeding, for example, a toy poodle with bad knees (luxating patellas) to a Yorkie with bad knees (also a breed prone to luxating patellas), you get mixed breed puppies very, very likely to have bad knees.
But I'm just using poodles as an example, every breed has genetic conditions that need to be tested for and considered carefully when breeding. It's important to point out that golden retrievers have serious problems with cancer, and almost every Cavalier has a terminal, genetic heart disease. Half of all Cavaliers show symptoms of this by only five years old - almost all are suffering symptoms by ten. I'm not saying these are bad dogs, just trying to emphasize how important it is to find a breeder who cares about health and is doing everything they can to make sure their puppies are as genetically healthy as possible.