Security of streaming replication? If I want to use streaming replication between two Postgresql databases on different parts of the internet, is there a way to secure or encrypt the connection between the two? Or are there reasons other than security to not do that?

I'd like to prevent eavesdropping via a man-in-the-middle attack.
Streaming replication in PostgreSQL uses the same security mechanisms as a normal frontend-backend connection.  So in order to encrypt the traffic, SSL should be used, and access control should be set up.

Alternatively, or additionally, consider a VPN of some kind.  PostgreSQL instances aren't really meant to be run facing the open internet.