What exactly are these "furries"? These folks?
(?)
spoiler (click to show/hide)

I can never un-see that.

Furries, afaik, are the dudes into anthropomorphic animal cartoons. Think about Disney's old Robin Hood movie with the fox in the title role, except with tits, or a penis, or both. I think
Omaha the Cat Dancer was the ur-furry or proto-furry source, with all kinds of furry comics in the wake.
Then there are plushies, who sexualize stuffed animals, either dressing up as stuffed animal toys or engaging in frottage with stuffed animal toys. I'm specifying toys because there are probably sexual fetishists who interact with taxidermy. Ew. God, I'm unhappy that my mind even went there.
Bronies are a subset of furry. The object of their obsession is a partially-anthropomorphized cartoon character.
The family in your picture are just weird, and possibly sick. I mean, why is the girl touching daddy's fake junk? Good god.