I was under the impression that refusing cash, otherwise known as legal tender, was illegal for a private business. It appears I was wrong.

Private businesses are free to develop their own policies on whether or not to accept cash unless there is a State law which says otherwise. For example, a bus line may prohibit payment of fares in pennies or dollar bills. In addition, movie theaters, convenience stores and gas stations may refuse to accept large denomination currency (usually notes above $20) as a matter of policy.
Source.

ETA: Be wary of paying with 2 dollar bills. Link.