HONG KONG—As thousands of protesters marched in their fourth mass demonstration in a month, their target is expanding beyond the city’s government to the more distant power they blame for their eroding freedoms: China itself.

Protesters marched mostly peacefully Sunday through a major shopping belt in Hong Kong that is frequented by mainland Chinese tourists, the first demonstration in recent weeks away from the area near Hong Kong’s government headquarters. The destination was a high-speed rail station that handles massive...