Question

why Might the United States have been concerned early in the Vietnam war about China's attitude towards US involvement on the side of South Vietnam

Answer 1

US didn't want a superpower entering the war-- China entering or aiding the war would have tipped the balance of power.

China's interest in Vietnam could have tipped the power balance in the war just as it had in the Korean War. Chinese money, weapons, or at worst, military aide could have led to a larger scale war. China and the USSR were allies and interested from a Communist country could have led to another world war or a more difficult regional war.

Answer 2

The Vietnam War occurred during the Cold War (best described as a lot of political and geographical tension between Western and Eastern powers after World War II). Since the US was on the western side (most often associated with capitalism) and China on the eastern side (most often associated with communism), the US might have been concerned about China's attitude toward the US due to its close proximity to Vietnam. If China were against US involvement, then the US would have another (more powerful) enemy to face in addition to Vietnam.