Someone told me that saying "Mach dir die Augen zu " is rude. He told me that to make it more polite say " Mach die Augen zu". Does using the reflexive pronoun "dir" makes it more direct? If the reflexive pronoun is removed it's like using the pronoun "man" ?
I personally would not consider this saying to be rude. Most of the times, using "dir" in this case is leading to a more specific result. For example:
This could basically mean that someone is supposed to close any jacket. It could even be one that he is not even wearing. It just says that someone should close a jacket and it depends on what the speaker is looking or pointing at whether he means the jacket the person is actually wearing.
This however is more specific. It definitely means that someone should close the jacket he is actually wearing.
Concering the eyes this is what I would conclude here: Because of the fact that someone is not able to for example close someone else eyes, there is no need in using "dir".
What would be said is
because it directly refers to the eyes of the person the speaker is talking to.
PS: One thing about that came to my mind because I was really thinking about this sentence to be rude.
This could actually be a rude sentence, because (depending on the context!) it could basically mean that somebody should die. Closing the eyes here could (!) refer to dying that is why this sentence could be considered rude.
However, as always, it is not that simple. It could also mean that somebody is supposed to close his eyes for receiving a present for expample and to be surprised afterwards. This really depends on the context.