Since FME 2013 this is no longer implemented, the Allowed Geometries field will strictly have to be set to 'postgis_none' in order to write to geometry-less tables.
Strictly speaking, the new behaviour is correct, of course. It however gives me a big headache changing all the dozends and hundreds of Feature Type Proberties in all my dozends of workbenches in order to make them running properly again...
When you make the change to one of these types, click the button at the bottom of the dialog marked "Apply to...". It will let you pick which changes you want to make (in this case the geometry) and also which feature types to apply it to.
That should make the process a little easier.
Another setting that may help, when you add a new writer look at the properties dialog and there is a setting called "Create Generic Spatial Columns". As long as that is checked the table should be a generic one and not need a geometry type set.
Hope this helps
Mark
Mark Ireland
Product Evangelist, Safe Software Inc.
http://screencast.com/t/93zP1d2yz1
Regards
Mark