I believe that because the outline pass is additive, it really only matches the given color well for fully-saturated colors. E.g. RGB = 1, 1, 0 will work, but RGB = 1, 1, 0.5 may not. Perhaps that could be changed/fixed, I’m not sure.
I’m not aware of any way to set an exact color for the outline. The effect may need to be customized, or you could file an issue or feature request on the post processing module.
For the background color — Any use of post processing will change how and where color management works, and works differently in three.js post processing VS. the separate pmndrs/postprocessing project. I think the quick fix would be to do convertSRGBToLinear() on your background color when using it with post processing.