At one point in the film, newspaper articles are shown onscreen to illustrate an large-scale event occurring. However, the articles refer to modern day Republicans such as Ted Cruz or Lindsey Graham, who could not possibly be politicians in the world presented in film.
The film states that the first fatherless pregnancies began in the 1950s, and the resulting change in the gender balance lead to the first female president of the US in 1965. However, no change in the proportions of male-to-female voters could occur before the 1970s.
The film tries to humorously imply that the men were too lazy to grow their own food, but 66% of crop workers are male, so this would be a simple initiative to implement in the sanctuaries as they had all the skills and knowledge to do make this happen. They also stated that there was plenty of idle time in the sanctuaries and guys were bored. Men would naturally continue their work as a hobby if not only to ensure untainted food. There are plenty of men who garden as a hobby, so it would make sense that at least a few of them would continue this activity.