1. It takes a woman to carry the gun.
Repeatedly, throughout the series, the doctor refuses to carry a weapon, yielding only his sonic devices. In season 9, the lore changed a bit, so instead of the characters never carrying weapons, only women carried. In one scene from episode 8, a man was even shown as unable to have enough discipline to be a good fighter, leaving it up to the women to come in and save the party. This dynamic often led to a role reversal of traditional male-female. The female characters in the show often had to fight to bail the doctor out of dangerous situations. In the Christmas Special, River Song even described the doctor as a "damsel in distress."
2. Women are powerful.
Beyond carrying a weapon, almost all of the leaders shown in the series were women, besides the doctor. Even if there was a male leader, he was usually foolish or got killed early on in the episode. In all of the episodes pertaining to crews, or groups (which is almost all of them) a woman is shown in power. Besides, in episode 7, only women are shown in charge of UNIT. Finally, in a personal favorite instance of mine, the stuffy old white man time lord stereotype is broken in episode 12. As per tradition, all of the time lords in power are shown as old white men. However, when one of them is killed and then regenerates, he transforms into a young black woman. She informs us that she is actually usually a woman, and that taking the form of a man was a rare exception for her. In episode 10, there is even a species introduced in which the females have exceptional gifts while the males do not. This could be easily overlooked as a coincidence, except that the males are actually described as "useless" by the doctor.
3. Men can be caretakers too.
Besides women fulfilling traditionally masculine roles, many of the men in this season filled traditionally feminine roles. Firstly, in episodes 3 and 4, a male character named Lunn fulfills a medical caretaker position for Cass, the group's leader. Medical caretaking is a traditionally female profession and is still dominated by women today. There is still a heavy stereotype in our culture placing women in a caretaking role, making this character unusual. Next, in episode 5, one of the most key scenes involves a man whose profession is extremely masculine (as a blacksmith) who stops his work in order to gently care for his baby. Not only is this scene heartwarming, but it is also important to show a man in a childrearing position. Finally, in episode 10, the protagonist Rigsy is shown caring for his child, with no mother present, much like in episode 5. In both cases, it is extremely unusual to show a man as a child's primary caretaker without any text depicting its peculiarity.
4. You don't need no man, but you can have one if you want.
Both Clara and Mistress Me are single heterosexual females who arguably don't need a man. They are incredibly powerful, strong, wise, and independent. However, throughout the series they have still been portrayed as sexually capable. Both are just coming out of long-term relationships, and have an interest in sexual lives. The most interesting part of their sexualities is that they both take on a dominant role in their relationships, being wiser and stronger than their male partners, but still stay sensually feminine. There is no abnormality to their dominant roles, and it in no way hinders them from finding male partners.
5. Testosterone is the enemy.
The most blatantly feminist message of the entire season is presented in 5. In this episode, emasculate characters are literally fighting against testosterone monsters using non-violent action. The best part is: they win. And if that's not feminist I don't know what is.
