¿Does anybody know if I can use pgpool as a balancer between 2 nodes that have BDR master/master configured for replication?
It's possible. In most cases I think it's probably going to be a very bad idea, though.
Most applications cannot just be pointed at multiple nodes and expected to work properly. BDR doesn't have a global lock manager or global transaction manager, so anomalies can occur that cannot on a single node. Applications must take extra steps to avoid them or be tolerant of them.
If you take an app that expects ACID semantics and READ COMMITTED isolation then, without it knowing, you send some of its transactions to each of two semi-independent nodes, you're going to get fireworks.
If your goal is write scaling, then it's not likely to do you a great deal of good anyway, because each node still has to apply the writes from the other node. So the writes still have to get done, just on another channel.
I'm speaking of the most general case, where I have no idea of what problem you're trying to solve or what your application is. If you can be more specific about the problem you're trying to solve by doing this and what the app does perhaps I can tell you more about whether/how BDR can help you, and if not point you to other solutions that might.
I have tried also Barman but does not work in logical replication and repmgr that does not work master/master.
repmgr doesn't understand multi-master and BDR yet, correct.
PgBarman works fine with BDR. It doesn't care that the database(s) it's backing up are BDR nodes. However you can't just restore a single node - to do a restore you have to shut the lot down, restore one node, then re-init new nodes from the one you restored.
