There's a race on the _participants variable, where it's being set in runCommit() and simultaneously read in reportState(). It's being set without a mutex, but read with a mutex.
Adding _mutex protection to where it's being set should be sufficient in this case.
I don't think there is any risk today of concurrent writers to any variables, because the TransactionCoordinator exposes a limited interface that can be called from the TransactionCoordinatorService, which itself is triggered when a command with a session and transaction number is run. However, since only one command with a particular LSID can be run at a time, there shouldn't be a risk of multiple commands with the same LSID being run concurrently, which means only one thread should be running on the TransactionCoordinator at a time, other than the reportState() case which is an exception.