Citing the Rev. Dr. Martin Luther King Jr.’s call to civil disobedience, 145 evangelical, Roman Catholic and Orthodox Christian leaders have signed a declaration saying they will not cooperate with laws that they say could be used to compel their institutions to participate in abortions, or to bless or in any way recognize same-sex couples.

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“We pledge to each other, and to our fellow believers, that no power on earth, be it cultural or political, will intimidate us into silence or acquiescence,” it says.

The manifesto, to be released on Friday at the National Press Club in Washington, is an effort to rejuvenate...