We had a long debate in my company around this subject. We came to the conclusion that the correct colour depends really on what we are trying to achieve.
NOTE: I take the point that colour alone isn't a great indicator due to colour blindness. In such cases, we combine colours with an icon shape.
If we are trying to use colours as an ordinal classification (...
For me the situation is not quite clear.
a) You offer software for others, who can do e.g. project management with it or
b) you work all together in your company with this software internally
For case a, you should leave it up to the others how they use colors. After all, a priority can also be represented with the colors.
For b it is not a matter of ...