What's a word used for someone who criticizes his country but doesn't let any foreigner criticize his country?

I don't think there is one word that encompasses both attitudes. Patriotism may lead nationals to frown upon external criticism and, indirectly, to their feeling that they are the only ones empowered or entitled (as @tk421 cleverly suggested) to speak as they wish about their domestic affairs.

This issue reminds me of a famous, long poem from my country, "Martin Fierro", which refers to the question in the following words:

Brothers should stand by each other because this is the first law.

Keep a true bond between you always, at every time --

because if you fight among yourselves you'll be devoured by those outside.

(Translated from Spanish by Kate Kavanagh)