Pitting him against villains prominently featuring red creates a strong visual contrast and reinforces the ideological conflict between Western democracy (as represented by Cap) and totalitarian Communism (represented by the "red" villains). It's a clear "good vs. evil" visual shorthand.
In essence, Captain America's long-standing conflict with "red villains" is a direct reflection of the geopolitical tensions and ideological struggles of the 20th century, particularly the Cold War, woven into the fabric of his comic book narratives