To me this is very political in its nature even though the government they support and tell other to support is only in their imagination it still opposes the
right of a country to get it citizens to bear arms in its defence, a very serious political stand.
Maybe, but as long as the federal goverment is not going after churches that explicitly call for election of certain politicians from the pulpit they are not going to go after anti-military religions. They'd probably have to go after the Quakers and Amish too if that was the basis. As long as Westboro Baptist Church still has tax free status despite hateful and much more overtly political speech than the WTS spouts, the WTS status is not going anywhere.
I don't discourage people from petitioning their member of Congress about this or any other issue they feel strongly about, but that is unlikely to be the way this kind of thing would happen. There is little to no political capital to be gained from such a move. People in general just don't care much, and there is always the risk that some voters would wonder if their church is next. If they did get a little too greedy and some fraudulent conduct could be shown, that would be a more likely trigger. Even then, I suspect they would try to somehow find a "fall guy" to take the hit and carry on unscathed.