Ana Navarro is known best these days as a co-host on ABC’s “The View,” but she isn’t likely to bring up the connection when she hosts an evening of the Democratic National Convention this week.

Although “The View” operates under the aegis of ABC News, Navarro is not held to the same standards as its full-time journalists, because she is an opinion-focused contributor to the program, according to a person familiar with the matter, not a traditional journalist who is expected to avoid any potential appearance of bias. ABC News declined to make executives available for comment, but...