I think these two changes are significant enough to the domestic history of the United States that it is at least quite reasonable to say that the Civil Rights movement would go on to develop very differently, and perhaps a lot later without these developments.
And I think that
neither of them is actually significant enough to make a very substantial difference to the timeline of the civil rights movement, or equivalently that there are countervailing factors that push in the opposite direction from the conclusion you want to make--for example, you mention the ties of certain civil rights figures to Communism, but Communism and left-wing thought in the United States was badly
damaged by the Soviet Union, not helped by them. The First Red Scare, which was closely tied to the formation of the Soviet Union, greatly weakened the political left wing in the United States through imprisonments, deportations, and other forms of political violence and suppression, and the association of many civil rights figures with Communism itself gave opponents of civil rights a powerful weapon to beat civil rights organizers around the head with. Moreover, the Soviets quickly established a vise-like grip on world Communist parties, which proved to be a serious vice; they were trying to orchestrate their activities from the point of view of Moscow, without much reference to local conditions. Thus, not having the Soviet Union around could very well
strengthen the civil rights movement, by making the left-wing in the United States stronger and removing the perception (and sometimes reality) of foreign ties from the movement. Frankly, I think color TV is more important than either the Soviets or World War II in spurring support for civil rights, and if anything that was
slowed down by the war.
Overall, what I see when I look at the history is a movement that was being driven largely by factors internal to the United States, primarily a reaction to the extremeness of the Jim Crow laws that were established in the late 19th and early 20th century, with factors such as the war--even taking into account the domestic effects of the war--and the Soviet Union and Cold War playing a secondary role at most. The effects of the formation of the Soviet Union and then World War II may have influenced the exact course of events somewhat, but by and large the actual movement seems to me to fit a larger pendulum pattern in American domestic politics between relatively brief comparatively popular attempts to spread civil rights and reduce oppression of African-Americans, like the previous period of Reconstruction, and longer periods of relative indifference by most of the white population and extreme hostility on the part of the South. The details most certainly would have been different, but I don't think the timeline would end up being all that different in the end, certainly not to the point of Jim Crow continuing for "decades" past when it ended IOTL or to the modern day. An interesting setting for a story, but it doesn't strike me as realistic.