Which word best describes someone who is coarsely ill-mannered?

The word "boorish" is the most appropriate choice to describe someone who is coarsely ill-mannered. This term conveys a sense of rudeness and insensitivity, characterizing a person who lacks refinement or social grace. Such individuals may exhibit behaviors that are offensive or unsophisticated, aligning perfectly with the description of being coarsely ill-mannered.

In contrast, "boisterous" describes someone noisy and energetic, often in a lively or exuberant way, which does not inherently imply poor manners. "Engaging" refers to someone who is charming and able to attract interest, while "amicable" describes a friendly and agreeable nature. Neither of these terms conveys the idea of coarseness or ill-manners, making "boorish" the definitive choice for this context.