TheNarrator is a common character type in stage shows. And frequently, the narrator's gender will be unspecified and irrelevant to the story. This trope is for those characters.
Examples of Gender-Neutral Narrator include:
The Leading Player fromPippin is perhaps the most well-known version.
The Balladeer fromAssassins, apart from being referenced as 'boy' once by Booth, could be played as female.
Only in the original staging. The revival, and most touring companies thereafter, require the Balladeer to be malebecause he's actually Lee Harvey Oswald.
The Narrator inAndrew Lloyd Webber'sJoseph and The Amazing Technicolor Dreamcoat is an interesting example: as written, the character has no specific gender, but is now always played by a woman to amend for the complete lack of female characters (other than Potiphar's Wife).
Not necessarily the narrator of the story, but the Book Voice of J. Pierrepont Finch's bookHow to Succeed In Business Without Really Trying in the musical of the same name could arguably fit this trope; in most of the productions it's usually a male.