Guessing its not much of a 'thing' in the US but in the UK you have a harness that goes around the dog onto a stiff bungee type cord. It plugs into the seatbelt and allows them to move around on the seat but stops them being launched through the window if you have a crash.

I'm not sure why anyone would be against protecting their pet like some of the other comments here though. Can't work out if its stupidity or ignorance.