Insurers in New Mexico must follow Obamacare protections regardless of changes to federal health-care provisions under a new state law.

Legislation signed by Democratic Gov. Michelle Lujan Grisham April 4 copies elements of the Affordable Care Act that benefit people with pre-existing conditions, among other populations. The state is one of a handful looking to enshrine the Obamacare elements supporters say are needed to make health coverage more protective and reliable for consumers amid the fear of federal changes.

New Mexico’s new law will prevent coverage denials or premium increases based on pre-existing conditions. House Democrats estimated more than 300,000...