Is it possible to backup and restore a materialized view with it's data?
Not really. You have to remember that pg_dump command creates simple CREATE TABLE and INSERT statements etc. So effectively when running pg_restore you're just running CREATE and INSERT statements on the server and inserting the data would require a "INSERT INTO MATERIALIZED VIEW"-command. That wouldn't make sense as getting the data by a shortcut would also danger the "integrity" of the view - you could insert invalid data on the manual restore process that the view wouldn't return otherwise. So I doubt that PostgreSQL would ever support manual restoring of materialized views data straight into database.

If you need to backup the actual data I would recommend using a table instead of materialized view and running a scheduled DELETE FROM/INSERT INTO statements to the table.