Churches have the right to publicly opine on matters of public policy. Even when such opinions happen to have startling alignment with certain political parties' platforms.
But here's an idea: when a religion starts actively campaigning for one party or another
, they lose the right to be recognised as a tax-exempt entity. Squared if they're doing it by lying.
You want to play partisan politics? You get to pay tax on your property and income, like the rest of us.