Depends on what you mean by “political.”  If you mean “Vote for Candidate X,” the answer is no.  If you mean “Don’t separate kids at the border,” the answer is yes.

The distinction is basically between lobbying and electioneering.  A 501(c)(3) organization, including a church, may not participate in an election campaign for a candidate for public office at any level, federal, state or local.  Although there is a serious effort to change the current law (See Ready Reference Page:  “Keep Charities Out of Politics”), 501(c)(3) organizations may not now support or oppose any candidates.  A “Vote for Candidate X” sign would jeopardize the church’s exempt status.  (See Ready Reference Page:  “IRS Issues New Guidance on Electioneering”)

A church, like other 501(c)(3) public charities, may engage in issue advocacy and lobby for or against specific or identifiable legislation (“Support H.B. 7816”), so long as it is not a substantial part of the church’s activity.  (See Ready Reference Page: “Lobbying Rules Create Opportunity for Charities”)  A church could support or oppose a referendum (which is considered lobbying since the general electorate functions as the “legislature” to pass the proposal) or a piece of legislation (“Repeal the Johnson Amendment”).  They don’t do it very often, but advocacy or small amounts of lobbying would not normally jeopardize their status.