I would say the most important theme in this short story, a feminist retelling of the Bluebeard tale, is that women can act in solidarity and triumph over adversity without needing male help.
In the original story, based on French folklore, Bluebeard is a murderous husband who has killed a series of wives. He marries again and says he must go off, giving his new wife a set of keys and saying she can use them to open every door in his castle but one. She opens the forbidden door, find the corpses of the former wives, and is about to be murdered for her disobedience when her brothers and a sister arrive to save her.
Carter's story follows the plot closely. The naive young bride is left alone in her castle, which, depending on the tides, is sometimes surrounded by water and sometimes not. The change comes at the end: the savior is the bride's mother, who comes galloping alone across now dry land to kill Bluebeard and liberate her daughter. The mother is a courageous woman and a good shot, and neither mother nor daughter need to depend on a man.
There are some pretty powerful themes in the story, and they are made pretty clear in the summary below. The coming of age theme is one that winds its way through all different places in the story and connects clearly to that of sex and added responsibility. As she goes to the castle, the journey might be considered a symbol of that transition, but it also starts the entire set of actions that drive her coming of age. The consumation of her marriage which starts her curiosity about sex and her use of the various roles of sex in her life continues to drive that theme of coming of age. It also begins to show the fact that she is not entirely innocent as she begins to delve into things that aren't considered appropriate, etc.