No and Yes. While cryptocurrencies held at Coinbase are not FDIC insured, USD cash deposits made by U.S. citizens are in fact FDIC insured up to $250,000 per individual.
Why would cash deposits be FDIC insured and not the cryptocurrencies themself?
This is because your Coinbase cash deposits are either 1) held in pooled custodial accounts with U.S. banks 2) they are invested in liquid U.S. Treasuries or 3) they are held in U.S. dollar denominated money market funds in accordance with state laws.
As of August 2022, the following depository institutions are where Coinbase customer USD funds were held: Signature Bank, JPMorgan Chase, Cross River Bank, Silvergate Bank, Pathward.