I purchased a new bottle of Emu Oil (skin), and the oil seems totally different from the previous one. The old one was more yellow and had a thicker consistency. While the new one is a very pale yellow, more like an off-white with a thinner consistency. Why the difference?

It depends on what the emus are fed.

Corn gives a yellow color to the oil.

If they are fed fewer saturated fats and more unsaturated fats, the oil will be more liquid.