My dog still triggers allergies from a friend who is very allergic to dogs, but it’s a poodle mix and poodles are supposed to be hypoallergenic? Why is this?

No dog is totally hypoallergenic. Hypo means less, not none. So while people with mild dog allergies may be fine around hypoallergenic dogs, if a person is sensitive enough, he/she may still be allergic. Also, if your dog is some sort of mix between a hypoallergenic dog and a non-hypoallergenic dog, there's no way of knowing whether your mixed dog will be hypoallergenic. Truthfully, the only way to find out is to have someone who's allergic to dogs stick their nose in the dog's coat.

If a dog is non-shedding, shouldn't it also be hypoallergenic?

Not necessarily. The allergen on the dog is the dander, not the fur. So even if a dog is low shedding may still release dander into the air which is what actually triggers an allergic reaction.

My dog is non-shedding but I still sometimes find its hair around my house.

No dog is totally non-shedding (unless your dog is hairless). You'll notice that even humans, who don't shed, who have hair will find their hair all over the house, whether it's after brushing or after taking a shower. The low-shedding dog is the same. It's going to drop hairs from time to time. The difference between a supposedly "non-shedding" dog and a shedding dog is that a shedding dog actually needs to change its coat every so often so it lets go of old fur and replenishes it, whereas with a "non-shedding" dog its fur just keeps growing and growing and growing until someone cuts it.

Adopt/Rescue vs. Buying from a breeder

While this particular "question" doesn't have to do with being hypoallergenic or low-shedding it does have a lot to do with picking a dog. Many times, this question goes hand in hand with what type of dog you want (ie hypoallergenic, non-shedding, etc.) and so I'll answer it. I will personally promote adopting or rescuing a dog from a local shelter. But I also understand the appeal of buying a puppy from a breeder. My reason for promoting shelters is because there are so many strays and abandoned dogs that need a home and there's a lot of variety at shelters, some dogs even come housebroken! Also, dogs from good shelters tend to be cheaper. Many of these dogs will be put down if they aren't adopted quickly, not because shelters are cruel, but because they need more room for all of the incoming dogs they get, and they want to give every dog a chance. Buying from a breeder is appealing for many reasons - you can choose the exact dog you want and you will almost inevitably find one, you get a cute little puppy, and usually, this dog hasn't had a past that a shelter dog may have had (like abuse). But keep in mind, that when buying from a breeder, not only is it more expensive to buy the puppy itself, but puppies are a lot of work to maintain. Also remember to buy from a reputable breeder, don't buy from a puppy mill, because sometimes these dogs have issues or weren't bred properly, which leads to problems like abandonment and not wanting to keep the dog.