Singularity
Infinite Density
You forgot at least one.
No, I'm not warmonger who feels the need to agree with obvious red herring from those with similar political ideologies.
But the question wasn't whether you supported all the people who supports the troops or whether you're against a particular war. I my mind you're going far beyond the original and seemingly simple premise of supporting the troops.
I don't support anybody whose beliefs I feel are contrary to the basic tenets which this country was founded. I draw your attention in particular to the First Amendment. It is the right of any American to dissent to anything which he feels is unconstitutional, much less morally reprehensible. The supposed hurt feelings of ostensibly professional soldiers shouldn't even enter the discussion.
That's close to a revolutionary tenet of beliefs though. Ideally a military is the arm of whatever democratically elected government rules. And if you think there's a systematic fault somewhere that doesn't allow you to influence it any more you're opposing the very fabric of your government on all levels of executive policy. Which should fit to the last point on my list of opponents. One man's revolutionary is another man's terrorist.