As worries emerge about the delta variant and the J&J shot, health officials — and, so far, the research — say the vaccinated are still protected

The delta variant is already the most dominant strain of the virus in some U.S. states, and that’s putting some Americans easing back into “normal” life on edge.

This variant, which was first identified in India in December, now makes up nearly half of COVID-19 cases in some regions and one-quarter of cases in the U.S., based on virus samples that have been sequenced, according to remarks made Thursday by Dr. Rochelle Walensky, director of the Centers for Disease Control and Prevention.

Delta’s takeover in the U.S. is inevitable, but it’s...