Final answer:
Fibromyalgia is the chronic illness that can make individuals hypersensitive to touch, thus affecting sexual functioning.
Step-by-step explanation:
The chronic illness that may affect sexual functioning by making men and women hypersensitive to touch is Fibromyalgia (D). Fibromyalgia is a condition characterized by widespread musculoskeletal pain, fatigue, and tenderness in localized areas. It is known to make individuals hypersensitive to various stimuli, including touch, which can complicate intimate relationships and sexual health. Other disorders, such as Diabetes and Multiple Sclerosis, also have an impact on sexual function, but not specifically through hypersensitivity to touch.