To define "unDursleyish," we need to define "Dursleyish." "Dursleyish" is an invented word to describe people like Vernon and Petunia Dursley. The Dursleys were Harry Potter's aunt and uncle who adopted him after his parents were murdered by Lord Voldemort.
The Dursleys' biggest obsession in life, after spoiling their son Dudley, was to keep up appearances and be seen as wealthy, successful, and completely "normal." This meant keeping their home and garden in impeccable shape, ensuring that they never made a single social faux pas, and creating an image of wealth. They are portrayed as extremely impersonal people who don't really care about anyone other than themselves.
To be "unDursleyish," then, means caring more about people than about appearances, not being fussed about what other people think of you, and being genuinely concerned about the well-being of others.