What sort of word would conjure up the idea of godlessness without pulling up the agnostic -atheist word loving lobby
Since atheism and agnosticism (or at least considered versions thereof) are both a product of critical thinking and skepticism, I'd vote for skeptic.
Of course if theism and/or belief in the unsubstantiated were not dominant in society, we would not find a label for its opposite useful, any more than we have a need for label aphilately (not collecting stamps).
 mordant
                                                
                                                Level 8
                                                May 27, 2018
                                            
                                                
                                                    mordant
                                                
                                                Level 8
                                                May 27, 2018                                            
                                        Or kafir.
 Stealthbeard
                                                
                                                Level 5
                                                May 27, 2018
                                            
                                                
                                                    Stealthbeard
                                                
                                                Level 5
                                                May 27, 2018                                            
                                        had to look that one up infidel or unbeliever - I like unbeliever.