Not accepting cash should be against the law.
Discussion
It technically is in the US but there are loopholes in everything now as well as the fact that the laws are only followed when it's convenient or beneficial.
If you pay and leave, you'll have a good standing in court. Best to prove that you paid though.
Even better, is to only do business with entities that are respectful. If they don't want cash, blacklist them.
When I see this list of payment methods I always think, is that all?