story identification - Time travel film: character with male and female reproductive organs is taken back in time by a barman who turns out to be themselves

I have had a friend give me a rough description of a film and I'm curious to find out what it actually is. I don't know very much. I understand this will be difficult, especially since every time my friend explains the tale it's different so this description is likely to contain some inaccuracies.

The film's plot begins with a recounting given by the main character, who had both male and female reproductive organs but had one set removed (not sure which, think male ones were removed). The main character is narrating this tale to the barman in a bar. The barman then takes the main character back in time, where they make love to themselves and produce a child.

The child, once born, is abandoned by the mother in the past - but the barman takes the child to the orphanage and leaves them there, ensuring their survival. Eventually it is revealed that the child was the main character themselves, and so was the barman.

In other words every major character introduced up to that point was the same person who had severely messed with their own timeline.

Answer

The movie was called Predestination (Wikipedia, IMDb), released in 2014, starring Ethan Hawke, and is based on a 1958 Robert Heinlein short story called "All You Zombies" (Wikipedia).

From IMDb.com:

For his final assignment, a top temporal agent must pursue the one criminal that has eluded him throughout time. The chase turns into a unique, surprising and mind-bending exploration of love, fate, identity and time travel taboos.

The main character is narrating this tale to the barman in a bar.

The agent moves to 1970 New York. As a bartender, he starts a conversation with one of the customers. The customer, John, writes true confession articles under the pen name "The Unmarried Mother". This pseudonym is explained by his own life story, which he tells the bartender. (Wikipedia)

The barman then takes the main character back in time...

The agent offers to take John back to the day that Jane met the lover who left her, so John can take revenge and kill him for ruining her life. (Wikipedia)

where they make love to themselves and produce a child.

While waiting, he encounters Jane, and when they begin talking, John realizes that Jane's lover was him. (Wikipedia)

the barman takes the child to the orphanage and leaves them there, ensuring their survival. Eventually it is revealed that the child was the main character themselves, and so was the barman.

The baby born from this "self-fertilization" is stolen by the agent and brought to the orphanage 18 years earlier, in 1945. Therefore, Jane, John, and their baby are the same person, revealing a predestination paradox. (Wikipedia)