In the OP I simply state that the Muslim Brotherhood is a political movement and an ideology is associated with it. I make the same claim for Planet of the Apes being a political satire. While different episodes may highlight different issues. There is no denying by ant thoughtful person that political messages are delivered.

this is not my interpretation it is widely written about, so here is a link that comments on each episode.

https://screenrant.com/war-planet-apes-politics-immigration-racism/

first paragraph follows.

“Let’s get one thing out of the way right up front: The Planet of The Apes franchise has always been political, and not just in the way that any story about dystopian societies are innately political. From the start, the Apes films (with the possible exception of the non-canonical Tim Burton-directed installment) have made an extra effort to frontload their narratives with pointed messages that often addressed the most controversial social topics of their day; in keeping with the common focus of the sci-fi genre of the era on using fantastical themes (see also: the original Star Trek, The Twilight Zone, etc) to symbolically explore real-world topics.”