It's a grey area. And a lot will depend on the reasons for the tax exemption in the first place. The common assumption is that they cannot use tax exempt funds for direct political purposes. ie supporting named candidates or parties. But even this is not 100%
I somehow sense given the recent timings that this is some saber rattling regarding the Catholic Bishops taking a hard stand against the current administration. I have even heard some threats regarding the churches "Tax exempt" status. What few realize is that unlike a "non profit" organization where the status is specifically "granted" by the government, in the case of organized religions the government does not have the legal authority to tax them. The only thing the government can do is early on make a determination to recognize something as a valid and recognized religious group. Once recognized the religion is shielded from further government action by the constitution. Every election cycle there is often a bunch of talking head chatter and cluelessness whenever a church has a candidate speak as to whether that would threaten their tax exempt status. The truth is it won't and it cannot. Any attempts to tax the church for such activities would fail a first amendment test easily and quickly.
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"

ou're not just a regular moron
You were designed to be a moron!"