Stay out of what?
The Brits were dragged into the war by the attack on Belgium. To break their promises would have been to lose face and look like they were ripe to be attacked.
Not to mention, Wilson left the Lusitania unavenged for two years, and even worse, got re-elected on the craven slogan “He Kept Us Out Of War”.
Britain should have “Brexited” back then. She had her Empire, why was she worried about the Continent?
“Wilson left the Lusitania unavenged for two years,”
The Lusitania was a British ship. And it was carrying a large cargo of war munitions. And the Germans took out an ad in the New York Times saying it was a legitimate target of war as a military cargo vessel. They warned everyone that they would sink it if they could.
There was nothing to avenge.
By the way, at that very moment we were a neutral nation. And the Brits were poised, ready, and certain to attack any American merchantmen that wanted to go to a German port.
The Brits were the bad guys of WWI.
There was nothing to avenge with the Lusitania; we were violating neutrality and shipping weapons on an ocean liner. German embassy workers with placards warned Lusitania passengers that the ship was taking weapons into a war zone.
We should have declared war on Britain; they blockaded the German coast and wouldn’t let us (as a neutral) trade with them, then complained when Germany tried to prevent our trade with Britain in the only way they could.
I live with a dozen miles of two munitions plants that were targeted by German sympathizers when we were feigning neutrality; both the Canadian Railway Car Company in Lyndhurst NJ (nice cover name, no?) and Black Tom Island in Jersey City NJ were destroyed because they were making weapons for Britain (again, while we were neutral).
Compared with the outcome, it would have been a small price to pay for Britain. WWI basically was the end for the British Empire.