They would be prohibited from not just ENDORSING a candidate or party or piece of legislation, they would also be prohibited from engaging in ANY advocacy for/against a candidate, party, or piece of pending legislation.
Of course taxpayer funded Pacifica Radio and NPR and PBS and other 501c3s violate this all the time (I saw Green Party literature in their "organizations" handout materials. If a church did that, the ACLU would be seeking to have the church stripped of its 501c3 status.
Untrue. A 501(c)(3) can advocate against a party & can certainly advocate for or against legislation, although there are limits.