Why do the rings glow yellow for Shang-Chi?

Cosmic energy is gold, which is the color of the Ten Rings once taken by Shang-Chi. (Shang-Chi’s father, Wenwu, wore the Ten Rings when they were blue.) Gold is also the color exuded by the Eternals, which hints the Ten Rings belong to them. “All their powers are gold,” opines the host.

Why are the rings blue when Wenwu uses them?

Because they glowed yellow when Ying Li took control of them too. Or they recognize the user’s mood, and take color accordingly. Wenwu had become greedy in his search for power, violent in his executions; unlike Shang Chi or Ying Li who had more peaceful intentions.

Are the 10 rings related to the Eternals?

The Ten Rings, after all, are circular in design, like much of the technology utilized by the Eternals. They also appear to be energy-based in their use, much like the tools and weapons used by the Eternals are fueled by cosmic energy.