Like all other religious texts, the Bhagwat Gita is allegorical and lends itself to dual interpretation.
On one level it is a very mundane historical drama which graphs the interplay of the righteous Pandavas and the devious Kauravas. Read from this reference point the exhortation of Lord Krishna to Arjun to take up arms against his very own kinsmen to gain back lost land and prestige is seen as realpolitik at its very worst. Or sheer wordly-wisdom of life's battlefield.
Dharma or duty inherent in life-circumstance of a person is what Krishna holds as the supreme arbiter of morality. Hence a soldier has to fight and kill if enemy attacks his motherland. Right has to be acquired with might, if need be.
It is such a world-view which leaves Gita open to charges of extremism. A world-view which justifies violence as a means to fulfill one's dharma.
But Gita is an esoteric text. It is esstentially a handbook of self-realization. The characters of Mahabharat are both at once, historical and allegorical.
Sudied from this point of view, Gita depicts the eternal battle between the good and the evil tendencies which goes on within each one of us.
If Kauravas symbolically represent our innumerable evil habits and tendencies then Pandavs are symbols of our few good and strong 'samsakaras.'
When Krishna tells Arjun to take up arms against the enemy and kill it, it refers to the 'fight-to-finish' battle which each person must undertake in his journey to self-realization, or mere better life.
This dual philosophy is what makes Bhagwat Gita an enigma. A text which is open to multifarious interpretation. The Gita has been variously positioned as a religious ritual text, as a handbook of vedantic philosophy, as a textbook of devotion, as a manual of yoga, as a book of modern management, among other things.
Now it has been anointed as a textbook of extremist philosophy. Not bad for a 5000 year old manuscript.