No they're real. Some people are just extremely passionate about disliking cars, mostly due to environmental impact vs the greener alternatives although there are likely other reasons too.
How does this work for the exit node? Surely they'll just get their IP flagged for torrent data? Or is the intention the data is encrypted so by the time it exits, nobody knows what the data is?
Also, does this turn everyone into a potential exit node too?
Most decent routers should support that. I personally use a Unifi Dream Machine which I can't fault. Previously used a Nighthawk router which also supported it.
Do you have any other requirements for the router? Or just to be able to run a VPN? When you say VPN, are you looking just to encrypt your home network (create your own VPN) or to use a paid service? E.g. VPN client or server?
Why?