I can't give you an answer based on ideology because the fact is that both sides decided to ignore ideology for geopolitical reasons. The U.S. and China both decided that the U.S.S.R. was a greater threat to them than they were to each other.

From the Chinese perspective: The U.S.S.R. was very near and therefore quite threatening. The U.S. was faraway and mostly concerned with countering Soviet influence.

From the U.S. perspective: China was much weaker than the U.S.S.R. and therefore less of a threat. But China was an annoying thorn in the U.S.S.R.'s side.