Final answer:
The Allies intervened in the Bolshevik uprising due to the threat of communism spreading, to protect their geopolitical interests after Russia exited WWI, and to support the anti-Bolshevik White Russians out of ideological opposition to socialism.
Step-by-step explanation:
The Allies intervened in the Bolshevik uprising because they were concerned about several geopolitical and ideological factors. The Bolsheviks, led by Vladimir Lenin, not only withdrew Russia from World War I through the Brest-Litovsk Treaty but also threatened to spread communism internationally which opposed the capitalist interests of countries like the United States and Britain. The Allies were already intertwined in a complex web of alliances that dictated military action to protect each other's interests. They were also alarmed by the prospect of Germany gaining an upper hand in Eastern Europe, which would have been a geostrategic disadvantage.
Furthermore, after the Bolsheviks successfully seized power in 1917, a civil war ensued between the Bolshevik (Red) and anti-Bolshevik (White) forces. The Allies, including the United States, sent troops and support to aid the White forces, due to their anti-socialist sentiments and concern over the threat of a domino effect of revolutions across Europe. This period of Allied intervention in Russian affairs created long-lasting suspicions and fueled the underlying tensions that would later manifest during the Cold War era.