With the latest release of Adobe XD, it's even easier to change object colors using the new eyedropper shortcut.
Simply select the object or groups of objects on the design canvas — so I'll come in and select this group — and then double-click to get into that rectangle. I can see it selected here on the right-hand side. And from there just type "i" on the keyboard to bring up that eyedropper shortcut. I can then come in and select any absolute color I see on the design canvas, so even if I were to come to the skin tone of this photo here, I can apply that color. I wouldn't be able to select a linear or radial gradient.
And if the object that I'm applying the colors to is locked it's not going to make that change unless I unlock the object. I can always come in and apply the color in bulk by selecting a number of objects. Let's say I come in and select all three of these rectangles. Once again, I type "i" on the keyboard and I can come in to select a different color and apply to all three. Let's say I did that one more time, I came in selected all three of these objects, type "i" on the keyboard and change my mind — decided I didn't want to use the eyedropper tool. All I need to do is hit ESC on the keyboard to step out of that mode.
I encourage you to give this productivity feature a try.