RALEIGH, N.C.—As North Carolina lawmakers reconvened on Monday, protesters and supporters held dueling rallies aimed at pressuring GOP leaders to either repeal or retain a new state law that dials back protections for lesbian, gay and transgender people from discrimination.

Lawmakers passed the state law in March in an emergency session to head off a new Charlotte ordinance that would have allowed people to use the bathroom corresponding to the gender with which they identify.

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