I think this is the whole point of this pastor challenge. Under the First Amendment the government does not have the right to tax (to tax is to regulate behavior) the church. This would mean that the government may not take away a church's exempt status because the church is not subject to tax in the first place.
I believe I've already read that in some places that pastors cannot condemn homosexual behavior because it is "Hate Speech". This is an effort to manipulate the inner workings of the church to conform with the liberal agenda.
If this group can afford the lawyers, there's no way the IRS will allow the case to go to court - because they'd lose.
But supporting political candidates is not tax exempt. You cannot enjoy a tax-exempt income as a minister when you are actively working for a particular political candidate.