One potential synonym for the phrase "not generally accepted" is "nonstandard," which implies that the idea or concept deviates from the norm or common understanding. Another possibility is "unconventional," which suggests that the idea or practice is outside the typical boundaries of accepted behavior. "Controversial" can also be a synonym for "not generally accepted," indicating that the concept is highly debated and has not achieved widespread agreement. Similarly, "divisive" implies that the idea or concept has caused disagreement and division among the population. Lastly, "unpopular" is a synonym that suggests that the idea or concept lacks popular support and is not embraced by most people.