Only in relation to my personal experience speaking about my fella specifically:
While there is no such thing as a truly hypoallergenic dog, greyhounds are in the low spectrum for dander. I would have been happy to move if she had asked me to. This allegedly highly allergic woman came within less than three feet of my dog of her own volition.
Any time my dog is outside of my home, he is leashed. He NEVER goes off leash unless we are in a contained space, I never take him to public dog parks (I'll get to why in a moment) and when I take him to the breed only park we go to, he wears a muzzle if there are also other dogs there - who are also wearing muzzles.
My dog has a high prey drive. If it is small and furry and fast - or even just small and fast, he will at minimum stop and stare at it, at worst he will attack it - and he has never tried to pull off the leash to do so. I keep him away from cats, tiny dogs, and small critters, and control the environment strictly with regard to small children or babies. Someday a rabbit will come into our yard and he'll probably leave me a present by the back door - that's fine, but also where I draw the line.
Pretty much anytime I take him out anyplace, someone remarks on how well behaved and quiet he is, including in the store. His breed does not often bark, and are loathe to relieve themselves in dwelling areas (which they tend to identify as "kennels". He also gets a bath every three months and is brushed once a week, sometimes twice.