PostgreSQL replication has plenty of major users who stress it quite a bit, and it is over 6 years old by now and a lot of the underlying infrastructure is older than that. The direct predecessor of the current replication (warm standby with transaction log file shipping, usually with rsync) is from 2006. It was a lot of work to set up right but once we got it up running it worked flawlessly for our use case.

So with its over 10 years of history (6 of those in its current form) the built-in replication has gotten quite a bit of testing.