How likely does its truth seem on cursory examination?
The poster significantly begs the question, in that it assumes that each war can be attributed to a single cause. This is a gross oversimplification which will make the historians cross.
Its claim about atheistic communism does not follow from the premises, which if true are that a very small percentage of wars over the course of human history are caused by religion. It ignores all other possible causes of war and appears to claim that the non-religious remainder throughout history are caused by atheistic communism, despite the fact that it has only existed in any identifiable sense in the last century or so.
It implies that war is the prime cause of death and suffering. Death and suffering are inevitable for each of us with or without war. Disease is a major cause of mass death and suffering that requires no war or political/religious philosophy.
It is grossly propagandistic in tone and structure. This does not mean that it is wrong, but it is a very strong signal that any truth content is highly slanted to an agenda and should be treated with great caution. So yes, you are absolutely right to be suspicious of it.
