What you're describing is not a problem with religion.
Any regular 501(c)(3) non-profit would lose their status in a blink of an eye, but not them.
http://www.patheos.com/blogs/friendlyatheist/2014/10/12/past...
You do also realize that the IRS has agreed to investigate the tax status of churches participating in such protests? http://ffrf.org/images/jointmotiontodismiss.pdf
As opposed to what? An unintentional endorsement? They perfectly know what the law is and they choose to break it. They have been doing it for decades, because they know the IRS won't do anything.
Hundreds of churches have been caught doing it. How many of them have lost their tax-free status?
http://www.irs.gov/Charities-&-Non-Profits/Charitable-Organi...
In other words, your blame is misplaced.