FWIW, my church (we're mixed racially) does have a "support our troops" ministry, as do many predom. white churches in the area. Anyone can submit the name/picture of a serviceman/woman (doesn't have to be a church member) and about once a month, this ministry team gets together and boxes up care packages for them. You're right, sending packages has nothing to do with supporting or not supporting the war, but unfortunately, there are lots of people that don't see it that way.
I still think the issue with the black church (in general) is its focus on a Sunday morning/Wednesday evening experience - and that's it. We should be offering up a variety of ministries that focus on serving others even if it means partnering with our churches (showing unity within the black community but also within the body of Christ). I think we've all heard the sermons, now we want to "see it". We need to demonstrate Christ in action and not just preach about it.