I saw this book in the early 1990s. It's about a child and her friend, who is a creature that I think might be a possum. The possum-like family are grotesque, and have bad manners and hygiene. The illustrations were linocut or something similar, in a naive style. The message, tolerance and loyalty to friends, is not stated but clear.
Examples of naive linocuts: https://carryakroyd.co.uk/Publications/woodissweet.html