when using exeutil /mh those DB like Local Continuous Replication (LCR), Cluster Continuous Replication (CCR), Standby Continuous Replication (SCR), of the Database Availability Group (DAG) passive database copies appear in a dirty shutdown state. this is by design. Do not fear that.
the reason is dirty shutdown database indicates that the database requires additional transaction logs to be committed in order for the database to stand on its own. Those Lagged passive databases always get the log from active node a little later. And after get enough log the replay process will start. So it means those database will always in dirty shutdown status. So this is by design, right?