You can get geography into your OpenJUMP map by using the Run Datastore Query tool. Normal way to add datastore layers does not work because in that case OpenJUMP is reading the metadata from the geometry_columns table from the database. If you have a table with geography those metadata are naturally missing.
But no worry, the Run Datastore Query tool is very flexible.
First create a table for testing and insert some data
create table geogtest (geog geography, id integer)
INSERT INTO geogtest (geog, id) VALUES (ST_GeographyFromText('SRID=4326;POINT(-110 30)'),1 );
Next write a query that is casting geography into geometry and run it with OpenJUMP
Check the result
This way you can select and view geography data in OpenJUMP but you can't edit geography tables.