The Czar and his family weren't "murdered". The leader of the enemy faction is a legitimate target in war. Their lives aren't any more precious than the other nameless casualties of war who had no choice.

The Czar was personally responsible for the war in the first place. If he wasn't an inept ruler, his subjects wouldn't have risked their lives to rid themselves of him. Even at the last minute, he could have averted the war by simply holding elections, but preferred getting millions of his people killed stubbornly refusing to accept his rule was over.

His family wasn't murdered either. By the Czar's own monarchist logic, the moment he died a family member became the new hereditary ruler of the empire. Monarchists are the ones who make dealing with their children a necessary part of cutting off the head of the snake, and are 100% responsible for putting their kids in that position.

Russia would have been turned into Lebensraum in WW2 if the Czar was still in power, the people who joined the revolution were vindicated for making the right choice for their country and people.