As an active duty member, I would have to say you can't separate the two. It's like saying you support the players on "your" football team, and like the fact that they win all the time, but hate the fact that they actually play the game instead of just practicing all the time.
That is my view also. I know that when I was in the 1st Gulf War, my folks would write to me and tell me about such people.
I always thought they could go straight to hell as far as I was concerned.
My son who is currently serving in Iraq, feels the same way.
How can you claim to support the troops yet denigrate the job that they willingly signed up to do?
Sure there are some troops that signed up for the benefits and didn't actually have any intention of going into harms way. But I'm willing to bet that 98%+ troops support and believe in the mission, and resent those that condemn their mission.
To paraphrase a comment from my son,
You can't claim to support me while decrying that which I volunteered to do. I am here on purpose, and I don't need that "type" of false support.