You didn't ask about it, but let's just make it clear that being "unDursleyish" here means that a person is nothing like the Dursleys. With that in mind, I'm pretty sure that the use of "as" before and after the adjective implies some kind of comparison, in this case between "her sister and her good-for-nothing husband" and the Dursleys themselves (the most Dursleyish of people, I assume). So the use of "possible", along with the negative in "UNdursleyish", means that they are nothing like the Dursleys, that they - her sister and her good-for-nothing husband - just couldn't be (it is just not possible for someone to be) more different from the Dursleys than they already are.

Her sister was extremely un-Dursleyish. I can't say it better than that without using the words possible or impossible! Think of "As much as possible". Now "As un-Dursleyish as possible". Does that help.

I have not read the book , but, from the context ,' unDursleyish ' means that the sister and husband are so unlike to what a' Dursley' should be in the most possible way imaginable. Dursley is a family name, and it was made into an adjective to emphasis the inherent characteristic of this family , and the sis and husband dont have this characteristics