PostgreSQL: Dump consistant state without locking
Solution 1:
locking and locking are two different things. Some locks don't cause any problems at all and you can use the database as usual (access share lock), while other locks have a major impact and stop your business.
The most simple way to make a backup of a PostgreSQL database, is pg_dump. We make daily backups of a multi TB database, during business hours processing at ~2500 tps.
Don't compare PostgreSQL with MySQL, two very different databases. Many hard to fix problems in MySQL are very simple in PostgreSQL. Making consistant backups is one of those things.
You don't need a slave to make a backup. It's handy, but not needed.