Most cryptocurrencies are anonymous where the origin of coins is not known and transactions are also anonymous (this may not be 100% true but lets assume perfect anonymity). The society prevents criminalization (using the coin to commit or pay for crime) of cryptocurrencies by forcing the exchanges that trade crypto for fiat to adhere to Anti Money Laundering (AML) rules.
However this assumes that the criminal wants to convert to fiat currency. But what if there is sufficiently big economy for the currency (sufficiently big market, businesses accepting the cryptocurrency etc.), and the criminal can live without the need of fiat money? Can the society prevent this behavior somehow other than outlaw cryptocurrencies?
The only solution I can see is to request the use of governmentally issued electronic signatures to sign all transactions which would allow pseudonymity in a way that one would be identifiable to the government but not to the ordinary public crowd.