[rant]I have never understood why so much emphasis has been put on the belt used to show rank, etc. I get told that the "long" history (less than 80 years) of the belt being worn made it a "sacred" item of your uniform.
When Jigiro Kano-sensei started using the belts, it was so he and his students would know at what level they were by looking at the belt. It wasn't anything religious or special. He was at a point where he had a lot of students (most "hard arts" were illegal at the time, and many people were coming to Judo, both because of what he could do, and it was one of the few legal schools around at the time) coming on board, and he was no longer able to keep track of who was at what level, except his higher students. In one of the books he wrote on Judo, he stated that tools of the art - uniform, belt, etc - were to be kept clean, in good repair and neat. There was no forbidding of washing the belts. (In Japan the belts were washed as needed, as Japan was/is a fairly clean conscious country.)
In Judo, if you are doing things right, every person will hit the ground, on their back or their stomach, which puts the belt in DIRECT contact with the ground. Yes, if you are the person being thrown, your goal is to not hit the ground, but you will with time. Even if you through them instead and land on top of them to pin them, over half the pins will place your belt on the ground as well.
So the "history" of not cleaning your belt, and not letting it touch the ground isn't there.
As the belts started becoming cheaper and cheaper in quality, due to the desire to make more and more money by the vendors, it became an issue with washing the belts would cause them to deteriorate faster. To me, this is the only reason you don't want to wash a belt.
Your belt is a tool, a tool used to keep your gi closed and to show others in your school/style at what level of training you are at. That is all it is. It isn't endowed with powers of knowledge, it isn't something to be placed on a special pedestal (figurative or real). It is a tool.
These people that wear beat up, torn, ratty, dirty belts "because of the knowledge or history" in them deteriorate from the training of the art in my eyes. They are violating some of their very training and history in using torn beat up tools. If you want to keep it for nostalgia purposes, by a nice (why nice when the belt is all beat up?) rack and keep it on that. If your belt starts to get ratty, faded, and dirty, it is time to go back to the history of your art and keep your tools clean and fully functional by buying a new belt. (I have seen people get hurt by a torn, ratty belt falling apart in throws causing the person being thrown to land wrong as well!!)[/rant]