LT.WOLFE: I think in front of the men, it's necessary for me to give the orders.
Wolfe utters these remarks shortly after Barnes has given a litany of orders. Wolfe weakly attempts to assert his authority, but the politics of the platoon are such that Wolfe doesn't have a lot of say-so. The soldiers listen to Barnes, trust Barnes, and see him as their leader.
CRAWFORD: How come we always get f***ing ambush?
Francis: 'Cause it's politics man, politics.
This short exchange makes it abundantly clear that platoon politics have a lot do with who gets the terrible job of a night ambush patrol. In this case, it's all the guys in Elias' squad, who have to go out because of the large number of new guys. The vets and the guys about to go on vacation (many of O'Neill's guys) are politically protected.
TAYLOR: I figured why should just the poor kids go off to war, and the rich kids always get away with it?
Taylor describes the politics of the military draft (the "rich kids" always seemed to be able to avoid being sent to war), and says that he volunteered for political reasons: joining the ranks of the "poor kids" is his way of trying to remedy a gross injustice. It's a political statement, and a noble one, maybe. But we're betting he regrets it.
TAYLOR: The village, which had stood for maybe a thousand years, didn't know we were coming that day. If they had, they would have run. Barnes was at the eye of our rage, and through him, our captain Ahab, he would set things right again, that day we loved him.
Taylor illustrates the politics of the platoon. Barnes is in charge. He's the real leader, the one responsible for "setting things right" for his men, just like political leaders are entrusted with setting things right for their citizens.
BARNES: Elias is a water walker, like them politicians in Washington trying to fight this war with one hand tied around their balls. Ain't no need or time for a courtroom out here
Barnes hates politics, even though he's willing to play the political game. He associates politics with total incompetence, a messianic or missionary idea about war that refuses to accept the brutal violence necessary to win.
BARNES: You don't tell me how to run my war Elias… Out here you belong to me.
Barnes makes it clear that he runs the show, even though Wolfe outranks him. This is Barnes's war, and he can conduct however he wants. In a way, he's just like the American politicians back home, running the war however they want.
TAYLOR: I say we frag that f***er tonight.
Taylor utters these words shortly after Elias' death, and they reflect a big part of Vietnam War military politics, and the plot of the film. "Fragging," or the killing of a fellow soldier, was the war's counterpart to political assassinations, and guys like Barnes and Taylor are willing to eliminate their friends-turned-enemies to achieve their political ends.