The quality or state of being excessively sensitive or emotionally idealist is called

sensibility
sentimentality
sophism
stoicism

The quality or state of being excessively sensitive or emotionally idealist is called sentimentality. (Option B)

Sentimentality means exaggerated and self-indulgent tenderness, sadness, or nostalgia. It is  the expression of gentle emotions such as love, sympathy, or caring.

In terms of philosophy, sentimentalism is a view in meta-ethics according to which morality is somehow grounded in moral sentiments or emotions.