The imperial powers that were direct threats to the revolution and they were already fighting, buddy, aka the Ottomans and the Germans. Hey, remind me how that worked out in the end? Did the People's Government get a seat at Versailles? No? Had to fight a war against fucking Poland first and then get even more people killed by Germany later?
And your argument is "the decision was unpopular," not that it was wrong.
You also find that they were not overthrown. Their political alliance was couped, like what happens in a "real democracy" when you push an unpopular policy. Even then, they supported the Bolsheviks anyways in the civil war.
Generally speaking, it's considered rude to murder all of your fellow socialists anyways if that happens.