Can a Christian be a national citizen in the general understanding of the term? No.
To begin with, we are called "citizens of heaven". That is, we have a citizenship that is not of this world, or to this worlds powers. Therefore, though we are born as 'citizens' of a certain nation, this is only according to secular labels that are forced upon us, and not part of our true identity in Christ.
Christ's kingdom is made up of people from 'every tribe, tongue and nation'. Jesus says that those who are truly his 'mother, and brothers and sisters' are those who 'do the will of my Father in heaven'. Therefore, our familiar identity is found in Christ and those who belong to him.
Our family is diverse and spreads over the whole world. It knows no boundaries or borders and it's identity is not found in national allegiance, but in our common commitment to Christ.
The Scripture clearly warns us both against the making of oaths and dual allegiances. In Matthew 5:34-37 we are told that what we commit to and what we reject is based on our commitment to Christ rather than an allegiance to man made ideologies (based on various superficial, circumstantial, or temporal commonalities). James 5:12 reaffirms this.
Matthew 6:24 teaches us to stand clear of dual allegiances when it says “No one can serve two masters. Either he will hate the one and love the other, or he will be devoted to the one and despise the other." This verse finishes by stressing that one cannot serve both God and Mammon (name of a Greek god associated with wealth). While the context is warning against holding too closely to temporal comforts and pleasures, it certainly extends across the board. Therefore, one cannot pledge their allegiance to Christ and national interest simultaneously. One will always deviate from the other at some point, since their interests are not held in common. Since one seeks what is eternal and the other what is passing away. One seeks the common good and the other the good of a minority.
Therefore, those who serve Christ find their commonality and identity in Christ. The boundaries and borders are then found in Christ and not longitudinal and latitudinal lines. Therefore, our commonality cannot be both national and faith oriented. Faith is not bound by national identity.
Secondly, Christians cannot hold to a dual allegiance. To pledge allegiance to a temporal institution is to be at odds with the eternal institution of God. The two will often be founds at odds and operating according to contradictory principles. This is why a person cannot serve two masters. Not to mention that one cannot truly be sure that national interests are genuine and altruistic.
In conclusion, national allegiance often finds itself in opposition to allegiance to Christ, since it seeks its own good as the ultimate goal. Since the goals and ways of national interest are often at odds with the goals and ways of Christ, one cannot pledge allegiance to both without finding oneself divided and internally in contradiction to oneself.
The citizen of heaven ought to be considered an outstanding citizen wherever they find themselves. Yet this is not because of a spirit of national pride, but a spirit of love toward all people, motivated and directed by Christ. They become enemies of the state in-as-much as they refuse to stand with the state in their opposition to humanity. The state is constantly placing itself in the position of opposition against humanity by being 'against' others based on their temporal 'boundaries'.
And so, the citizen of heaven is a good citizen, but never a true citizen of national interest, since national interest regularly stands in contradiction to the interests of the Kingdom of God.