As per section 31 U.S.C. 5103 of the "United States Coinage Act of 1965" Federal law specifically says: "United States coins and currency are legal tender for all debts, public charges, taxes, and dues."
Even charging an extra handling fee for dealing with all the coins is difficult to justify given the wording of the law. Luckily, carrying around 5 wheelbarrows of coins is also inconvenient for the person who's doing the protesting, so you really only see this sort of thing when someone is really aggravated and has lots of free time and money, it's not like we have a rash of DMV offices being crushed under a singularity's worth of pennies.
[0]http://www.craftvinyl.com/page165 (He actually got the BBC to link directly to his site, wow, he just made another million I bet!)
Also: does the law imply that every public entity that you pay taxes to in the US must have a physical office somewhere that you can go pay with cash? Mind blown.