I prefer keeping religion out of politics, because I believe that religion more than other ideologies is damaging to society when it gets mixed up in trying to rule populations. at the same time, secular shouldn't dictate religious organizations. it's been decided by secular law that churches, as defined in a specific way, cannot endorse politics. non-profits are something else entirely in a legal way. you have to meet entirely different criteria to qualify as a 501c3. a lawyer could explain the difference better, I think.
eta: I think churches specifically (not religious nonprofits--iirc, something like the Salvation Army is considered a non-profit but not a church) aren't considered not-for-profit. but again, a lawyer would be better qualified to explain this.