Most troops oppose war.
Saying you are against the war but support our troops is, fundamentally, intellectually dishonest.
The way to catch them in their dishonesty is to ask the protestor "what is the job of the military."
One of three answers, IMO, is likely:
1. To make war;
2. To protect the country;
3. To provide humanitarian relief.
If the third answer is given, then you are dealing with a hopelessly brainwashed leftist moron who fails to draw any distinction between UN relief workers holding a bucket of grain and a soldier holding an M-16. Certainly, the individual believes the main purpose of the M-16 is to serve as the upright stake for a scarecrow in a field of grain.
If the second answer is given, they are hedging, because they know the first answer is correct, and they just don't want to go there. It would probably be necessary to lead them through a series of questions with the aim of getting them to either devolve to choice 1 or 3.
If the first answer is given, then they are sunk. If they understand the purpose of the military is to fight and win wars, then by opposing the war they are opposing the very function the troops are there to perform.
But suppose they insist the third answer is correct. Then, since they don't understand the purpose of the military, how can they possibly purport to support the people in the organization--"the troops"? It is simply a logical impossibility to support the troops without supporting what they do. To do otherwise is to invalidate these people as individuals.
Thus, if a protestor says they support the troops but don't support the war, they do not even have the strength of their convictions to admit they really support neither. If they are at least going to protest the war, they should have the moral fortitude to be intellectually honest.
But that's just my opinion.