SAN FRANCISCO — Jess McCuan walked out her door one recent morning to take her dog, Doc, for a walk. Suddenly, a white car zipped through the crosswalk, seemingly oblivious to human and canine alike.

The prospect of Boston’s notoriously congested and confusing streets being traversed by self-driving cars is prompting some to worry about safety and job security in the city. Earlier this year, Waymo ...