Which word can describe a state of casual indifference that may be considered improper?

The word "blithe" captures the essence of a state of casual indifference that may be seen as improper. It signifies a carefree, lighthearted approach to situations, often lacking seriousness or concern for potential consequences. This carefree attitude can easily cross into the realm of insensitivity or disinterest, particularly in contexts that may warrant a more thoughtful or serious demeanor.

In contrast, "thoughtful" implies a degree of consideration and attentiveness, which is contrary to the casual indifference described in the question. "Profound" denotes a depth of thought or significance, which would also oppose a sense of casualness. "Serious" specifically suggests a sober or earnest approach, again not aligning with the idea of indifference. Hence, "blithe" is the best choice as it embodies a state of untroubled happiness that may overlook the gravity of the situation.