Not often.
In public, we are required by regulation to be a-political.
On a daily basis, even soldiers in the same unit, who regularly trust each other with their lives, don't often talk politics. It really doesn't come up as a topic of conversation very often. Because a political debate could have a negative impact on the morale and unity of a group of soldiers. What unites us is MUCH more important than what divides us, in the military. That sense of unity is what keeps you alive and motivated in combat. And most people wouldn't be willing to risk that for some political debate.