BEIJING—Roy Jones, 49 years old, never thought a $14-an-hour job running social-media accounts for Marriott International Inc. would require him to know global politics.

That was before he used an official company account to like a post on Twitter Inc. from a Tibetan separatist group. The group applauded Marriott for listing Tibet as a country, rather than part of China, in an online survey.

Marriott...