It is safe to shut down a replication source server and restart it later. When a replica loses its connection to the source, the replica tries to reconnect immediately and retries periodically if that fails. The default is to retry every 60 seconds. This may be changed with the CHANGE REPLICATION SOURCE TO statement (from MySQL 8.0.23) or CHANGE MASTER TO statement (before MySQL 8.0.23). A replica also is able to deal with network connectivity outages. However, the replica notices the network outage only after receiving no data from the source for slave_net_timeout seconds. If your outages are short, you may want to decrease slave_net_timeout. See Section 17.4.2, “Handling an Unexpected Halt of a Replica”.
An unclean shutdown (for example, a crash) on the source side can result in the source's binary log having a final position less than the most recent position read by the replica, due to the source's binary log file not being flushed. This can cause the replica not to be able to replicate when the source comes back up. Setting sync_binlog=1 in the source server's my.cnf file helps to minimize this problem because it causes the source to flush its binary log more frequently. For the greatest possible durability and consistency in a replication setup using InnoDB with transactions, you should also set innodb_flush_log_at_trx_commit=1. With this setting, the contents of the InnoDB redo log buffer are written out to the log file at each transaction commit and the log file is flushed to disk. Note that the durability of transactions is still not guaranteed with this setting, because operating systems or disk hardware may tell mysqld that the flush-to-disk operation has taken place, even though it has not.
Shutting down a replica cleanly is safe because it keeps track of where it left off. However, be careful that the replica does not have temporary tables open; see Section 17.5.1.31, “Replication and Temporary Tables”. Unclean shutdowns might produce problems, especially if the disk cache was not flushed to disk before the problem occurred:
For transactions, the replica commits and then updates relay-log.info. If an unexpected exit occurs between these two operations, relay log processing proceeds further than the information file indicates and the replica re-executes the events from the last transaction in the relay log after it has been restarted.
A similar problem can occur if the replica updates relay-log.info but the server host crashes before the write has been flushed to disk. To minimize the chance of this occurring, set sync_relay_log_info=1 in the replica my.cnf file. Setting sync_relay_log_info to 0 causes no writes to be forced to disk and the server relies on the operating system to flush the file from time to time.
The fault tolerance of your system for these types of problems is greatly increased if you have a good uninterruptible power supply.