Or are there any episodes with a subtext relating to Transgendered themes?
Having watched every episode of the original series (repeatedly... almost ad nauseum), No episode of the original series deals with transgendered people or body swapping across genders. There are a number of episodes where people swap bodies (older -> younger, body A -> body B), but no gender swaps.
I have not watched all of the episodes of the revivals, but looking through episode lists, nothing stands out as dealing with transgendered people or swapping across genders.
It is important to remember that the original Twilight Zone episodes began airing in 1959. In the episodes aired, married couples were still depicted as sleeping in different beds. While the subjects of identity and its relation to bodies and appearances were explored, particularly in episodes like Number 12 Looks Just Like You, subjects of sexual identity were still too taboo for the era.
I really think Number 12 Looks Just Like You was a silent pro transgender people message. You can easily replace many phrases and words to make it about transgender people and it makes a lot of sense. If that is not true then I think it's really quite the coincidence.
Synopsis courtesy of Wikipedia:
In a future society, all young adults go through a process known as "the Transformation," in which each person's body and face are changed to mimic a physically attractive design chosen from a small selection of numbered models. The process gives everyone a beautiful appearance, slows deterioration due to age and extends a person's lifespan, and makes the recipient immune to any kind of disease.
Eighteen-year-old Marilyn Cuberle decides not to undergo the Transformation, seeing nothing wrong with her unaltered appearance. Nobody else can understand Marilyn's decision, and those around her are confused by her displeasure with the conformity and shallowness of contemporary life. Her "radical" beliefs were fostered by her now-deceased father, who gave Marilyn banned books and came to regret his own Transformation years earlier, committing suicide upon the loss of his identity. When Marilyn becomes upset, talking about how the transformation makes everyone beautiful and therefore the same as everyone being ugly, they offer her a glass of "Instant Smile".
Despite continued urging from family, doctors, and her best friend, Marilyn is still adamant about refusing the operation. She insists that the leaders of society don't care whether people are beautiful or not, they just want everyone to be the same. Her pleas about the "dignity of the individual human spirit" and how "when everyone is beautiful, no one will be" have no impact. After being driven to tears by the inability of anyone to understand how she feels, she is put through the procedure and (like all the others) is enchanted with the beautiful result.