Final answer:
President James Monroe warned European nations to stay out of Western Hemisphere affairs with the Monroe Doctrine, and President Theodore Roosevelt expanded this with the Roosevelt Corollary, which allowed U.S. intervention in the region to maintain stability.
Step-by-step explanation:
The person who warned European nations to stay out of the affairs of the Western Hemisphere while also stating the United States would stay out of European affairs was President James Monroe. This principle was known as the Monroe Doctrine, which was declared in 1823 as a key aspect of U.S. foreign policy. The Monroe Doctrine received a significant addition with the Roosevelt Corollary in 1904, articulated by President Theodore Roosevelt, which stated that the United States would intervene in the affairs of Western Hemisphere nations if it was deemed necessary to maintain peace and stability.
Furthermore, the Monroe Doctrine reflected the United States' attempt to avoid permanent entanglements in foreign alliances, a stance originally advocated by President George Washington. The Roosevelt Corollary evolved the doctrine by allowing the U.S. to act as an international police power within the Western Hemisphere, thereby setting a significant precedent for U.S. interventionism in the region.
Despite attempts to steer clear of European conflicts, the U.S. found itself acting to prevent European influence in the affairs of Latin American nations. The doctrine and corollary marked a turning point in American foreign policy and highlighted the U.S. as a rising power with vested interests in the affairs of its neighboring countries.