I can't see how soldermask color would affect placement either, especially not if you place fiducials (or if the fab places them for you!)
For actual production design like the OOP is talking about, you would likely go with whichever option is cheapest overall (which in my experience has universally been the standard green).
Fiducials are automatically placed in top copper, but we also noticed larger misalignments of paste and smaller 01005 passive components (pre-reflow) on non-standard colors. Again, unlikely to cause large yield problems unless you've got a lot of components, but why risk it.
We did still use red for test PCBs so that they wouldn't be shipped to customers. If we were making gaming video cards colors would have been more of a priority.
If I want mega-cheap, green is good. If I want reliability, almost any other color is better.
Where I seem to see issues with green soldermask coverage are tented vias underneath components.
The canonical example is a non-GND via underneath a QFN component with a pad. However, I have also seen issues with vias next to large pads of power transistors where the transistor can "float" around on the solder.
This seems counterintuitive since I would expect the main soldermask color to be used for more BGA-type components where the breakout vias would need to be covered properly. Nevertheless, experience suggests otherwise.
I finally got fed up once and ordered the same PCB with green soldermask for one batch and blue for another. The green ones had some via coverage fails; the blue ones didn't have any. Since then, I've just avoided green soldermask unless I'm going for uber-volume levels of PCBs.