For Snoke, the loss of the Starkiller Base was as significant as his wins. His forces are no longer a secret to the galaxy at large. Those who used to laugh at the idea that The First Order was a threat are either dead or no longer laughing. The Cold War-style standoff is publicly over after the full-on assault on the Republic and the senate. The galaxy no longer views Snoke as someone that is irrelevant on the galactic stage. The galaxy knows he and his cronies are maniacal zealots and they should be feared for better or worse. The galaxy seems to mostly understand that the First Order is eventually coming to conquer its worlds and those worlds have to fall in line or resist. Most understand that war has returned and the perceived era of peace is over.
Snoke understands that everything the First Order used to do in secret is no longer an option and a very overt war is on the horizon. Unfortunately, The Republic has completely collapsed after being attacked by Starkiller Base in Star Wars: The Force Awakens. The galaxy is in complete disarray. The galaxy understands that everyone has to pick a side now.
General Organa no longer stands alone in her determination that the First Order is the greatest threat to freedom and democracy in the galaxy and the only choice they have left is to fight.