Said Hufflepuff, "We'll teach the lot. And treat them just the same."
This isn't saying anyone could be a Hufflepuff. The focus is on "treat them just the same."
Helga Hufflepuff expected her House to be willing to treat everyone with kindness. If you won't, then you can't be a Hufflepuff.
She was willing to teach anyone.
To be a Hufflepuff, you need to want to be taught. You need to want to be kind to others.