I've put my red mats in the washing machine before and they came out fine, im pretty sure Dotty, Porthos and a few others have done this before with no issues. They're a bit of a squeeze depending on how big your machine is, and you have to kind of fold them in around the edges to fit, they'll come out with big creases in them but they fall out quite quickly.
Another thing you can do to try and get them looking new again is if you have a few grades of fine sand paper 1500 grit and up etc... you can then sand the metal badges down and get all the scratches out. Porthos did this and they came out looking like new, i havent tried it yet myself though.