Not really, not in the Nazi Germany vs. USSR contest. Communism in the Soviet Union was highly exclusive and discriminatory, especially so in the war years; OTOH, Nazis were happy to accept everybody who'd join their war effort, even if they did a little ethnic slaughtering at one sector of a front while the ethnic group in question was fighting the Soviets for them at another.
A military alliance in this context of a contest would not be an ideological one. Churchill allied with the Devil because the Beelzebub was about to overrun his country; he'd have done the reverse in the reverse situation, and so would everybody else. Let's not forget that Hitler immediately won allies to his cause whenever he drove out a comparable danger from another direction. Stalin was but one such danger: Norway was about to be occupied by Britain and well knew it, lending a bit of legitimacy to a local Nazist movement, while the Balkan nations directly benefited from Hitler sorting out longstanding issues between them. It's not that Hitler would have been a solution: it's that, combined with the fact that Hitler was coming anyway, an alliance made a great deal of sense.
None of these alliances and arrangements really had a significant ideological element to them - it just obviously followed that after a deal was made, those with Nazi sympathies had a position of power in the ally nation. But perhaps tellingly, while there existed Nazi factions in several nations, and the war gave them disproportionate powers, no nation demonstrated a comparable increase of Communist sympathies due to the war or volunteered to join fates with the USSR. The "universal appeal" of Communism hit its lowest bottom at the time...