The answer to this question depends on the meaning of the word “patriotic.” As with many words, there are different nuances of meaning, and different people use the word in different ways. For example, at its simplest meaning being patriotic simply means “loving one’s country.” As long as that love for country does not supersede one’s love for God, and if it is kept in proper perspective, there is nothing wrong with a Christian being patriotic. However, another definition of “patriotic” implies that the individual should place the interests of the nation above his or her personal and group interests. Carried to this extreme, patriotism can become a form of idolatry, particularly if one’s love for his country is greater than his love for God and God’s plan of redeeming people from “every tribe, tongue and nation.”
As far as a Christian’s responsibility towards government, we know from Romans 13:1-7 that we are to be subject to the governing authorities and to honor them, even when they are not honorable, because it is ultimately God who has placed them in authority over us. So, as Christians, we are under obligation to God to be model citizens, subject to the governing authorities over us by obeying laws, paying taxes, etc. However, our responsibilities are first and foremost to be obedient to God. In America, a constitutional republic where individual citizens have the ability to change and influence government by voting or by being politically involved when appropriate and in appropriate ways, part of being a good citizen is voting and having whatever positive influence we can on government.
In countries where Christians have no say in the decisions of their leaders, it is more difficult to be patriotic. It is very hard to love oppressive governments. However, as Christians we are still obligated to pray for our leaders (1 Timothy 2:1-4). God will honor our obedience to this command, and in His perfect timing, He will judge leaders who turn away from Him. Should a Christian be patriotic? Within reason, yes. At the same time, a Christian’s ultimate faith, love, and obedience are to be reserved for God alone.