Donald Trump says that "an amendment, pushed by Lyndon Johnson, many years ago, threatens religious institutions with a loss of their tax-exempt status if they openly advocated their political views."
Trump's claim is mostly false - religious institutions often advocate their political views. What they can't do is advocate voting for specific candidates. Moreover, the law that Johnson pushed was not aimed at religious institutions, but rather at red-baiting McCarthyite organizations. Since the law covered all tax-exempt non-profits, it also covered religious institutions.
I think this law is actually very good for the churches. I expect my church and pastor to promote decency and justice, which sometimes mean taking a side in a political argument. However, that is different from endorsing or opposing specific candidates. Candidates are people with a mix of vices and virtues - some of which will only be revealed in the future. The potential for corruption in the short run, and embarrassment in the long run, of allying the church with specific candidates, is very great.
The current law, which was not made for or about religious institutions, has worked to our advantage.