There really shouldn't be any need to race-swap characters. Fallout isn't a character-based or narrative-driven series, it's primarily a sandbox setting that can be used to tell any story the writers can fit into it, just like in most RPGs like Shadowrun, The Elder Scrolls, and D&D's Sword Coast. There might be a larger meta-narrative at play, but that's really more to establish a proper history and timeline to tell the latest story in. Ideally, a Fallout TV series wouldn't need to adapt any of the games (and with it, do race swaps); it could just tell its own original story with all-new characters, rather than just adapt the story of one of the games.

Though yes, there is indeed going to be an absurd number of alphabet people regardless. Even though this is a setting where much of the population is going to be expected to bear children, and supposed trannies are going to have a hell of a lot more to worry about than whether or not they're in the wrong body or break "gender stereotypes."