My dog just sits on the floor, seats folded up, on a big old moving blanket. She's not tethered but she is old and just kind of flops over if the truck has to swerve or something. Never gets hurt. I agree that in a serious accident she'd be loose, but she's flat on the floor and unlikely to go anywhere unless the truck flips over - in which case maybe we're all dead.
I would never let my dog ride in the back of an open bed. She rides with me where it's comfortable. Otherwise she stays home. If I had to transport kids too then I'd have a super-awesome camper top, a rubber or carpeted floor, and a seal between the windows so the AC/heat can flow to the back too. When I had multiple big dogs and only an extended cab, that's how they rode. I only quit the camper tops after I got crew cabs with fold up seats and flat floors.
As far as dog hair, I don't worry about it. Vacuum the truck once in a while and tell anyone who doesn't like chancing that they may get a bit of dog hair on their clothes that they might prefer walking instead