What word would you use to describe someone who lacks the ability to feel emotional stimuli?

The term that best describes someone who lacks the ability to feel emotional stimuli is "insensible." This word connotes a state of being impervious to feelings, sensations, or understanding emotions — indicating a profound numbness to emotional reactions. An insensible person may not respond to emotional cues or stimuli, which aligns with the notion of lacking emotional sensitivity.

In contrast, "empathetic" refers to the ability to understand and share the feelings of others. "Callous" describes someone who is emotionally insensitive or unfeeling but doesn't capture the idea of a complete inability to feel. "Compassionate" signifies a strong awareness and concern for others' suffering, which is the opposite of the state described in the question. Thus, "insensible" is the most fitting choice for someone who cannot feel emotional stimuli.