As we're not told explicitly why everyone is uninterested in (or at least not mentioning) the contents of the letter, we need to use context clues to try to understand what is going on. These clues would suggest that the letter is sexual in nature.

We learn the following about the purloined (stolen) letter:

The document in question—a letter, to be frank—had been received by the personage robbed while alone in the royal boudoir. During its perusal she was suddenly interrupted by the entrance of the other exalted personage from whom especially it was her wish to conceal it.

A letter coming directly to a royal woman—a queen or a princess—in her bedroom while she is alone there would suggest it was from someone intimately known to her. This person must have had access to the royal's servants and been able to direct them to deliver the letter to the queen or princess when she was alone. For the servants to deliver the letter and the royal woman to accept it indicates she had a past with the sender.

We also learn that she is surprised when her husband enters the royal bedchamber—she obviously did not expect him to show up at that time. We also learn that she particularly wants to keep knowledge of this letter from her husband. All of this suggests that should the letter fall into her husband's hands, it would reveal an affair.

Now, we don't know for a fact that this is a love letter, but the delivery to a bedroom, the royal woman instantly starting to read it, and her extreme fluster when her husband comes in unexpectedly all point to a romantic intrigue.

We also need to keep in mind that the story was published in 1844, a period when it was not polite to talk openly about sex. The men involved in the story would have understood that it would not be socially acceptable to inquire into the specific contents of a letter that was probably sexual in nature. No matter how interested they might really have been, they would been expected to tiptoe around the subject matter and not be curious. Further, to publish his story, Poe would have had to hold back on graphic content about sex.

The point of the story has little to do with the contents of the letter and everything to do with Dupin's methodology and cleverness in being able to get it back.