Well - some of them provide political platforms to inform their members who to vote for. I think the IRS looked into this at one point, though it didn't go that well [1].

[1]: To this day, it's claimed that it was partisan and targeted only one party, when in fact all non-profits were looked into; it was just that certain non-profits, which attracted members of mainly one party, were the ones mostly engaging in such practices. That party, of course, made sure the IRS didn't have somebody (by not confirming anyone to the position - which is still the same today) to look into this issue; without that person, the law has no teeth, and they can continue to (illegally) promote their own politicians, in violation of the law for non-profit organizations. But they claim "free speech" rights and "religious freedom" rights...