It is possible to replicate an entire database, then change some
tables to not be replicable. However, when you create replicas, only
the replicated tables are included. You'd have to copy the
non-replicated tables manually. However, once you wree set up, it
should work.

I have a couple of replicated apps that include a non-replicated
table or two, and the only time I have to worry about it is when I
create a new replica (I have to remember to manually import the
structure of the non-replicated table).

You might also consider partial replication, though I've never
actually used it myself (except for empty partial replicas).