WASHINGTON—States will be allowed to offer less-comprehensive health plans yet still qualify for federal subsidies under a new Trump administration policy that will let them skirt key regulations under the Affordable Care Act.

The change, announced by the Department of Health and Human Services on Monday, marks a fundamental shift in how the federal government enforces the states’ administration of the ACA, accelerating a trend in which red and blue states can craft significantly different health-care policies under the same...