If it's about cleaning what you use and you don't use those facilities, then I would have to agree that you shouldn't be made to do it. Myself, I do on occasion use the dishes at the office, and in such a situation I would have found a way to eat without using them, rather than cleaning after some slob who can't be civil without being forced to do so.

That said, if I was your employer and everyone had taken your stance, even the ones who do use the kitchen, I would have simply taken the dishes and utensils away. At that point it's just people being unreasonable.