Mach gefälligst die Tür zu!
Gefälligst ist use for rude commands. If you use it you probably assume that your social position in the given situation is above your counterpart's. Here perhaps: parents commanding a child. Could also be one colleague in an office barking to another.
Mach die Tür ruhig zu!
Ruhig is used to signal that you agree with your counterpart's planned activity - if he or she should take it, but it is eventually his or her decision. Typical situation would be: somebody in the office would like to close the door, goes to the door and grabs it, then looks around in the office to see if somebody reacts negatively. A friendly colleague could say: "Kein Problem, mach sie ruhig zu."