There was no staying out. The British would be dishonored if they violated their promise to defend Belgium, and would have been eventually conquered if they chose inaction; and the Kaiser had declared war on the USA several times without any response from Wilson (the very notion of “a United States of Europe against America” was authored by the Kaiser).
The mistake was for Britain to ally with their traditional enemy, France, in the first place.
And as far as Belgium went, screw them, after what they did in the Congo, the Germans never did anything like that in their African colonies.
Belgium should have been divided between France and then Netherlands, anyway.