Will the exchanges lock accounts now? Are they required to by law? Or will their legal teams advise them to do so as a precaution?
Not unless they receive a written court order, and then, only if they are under the jurisdiction of United States' laws.
To my knowledge, both Bittrex and Poloniex are.
They consider jurisdiction to be anywhere a US citizen stands or where he keeps his money especially in regard to possible tax evasion.
Just ask Swiss banks that gave up all of the private ownership info of US citizens and companies who had bank accts with them.