No movement or religion is internally consistent in its full set of ideas. Especially religions. You'd have to have a movement that is really single mindedly focused on one thing and very fundamentalist, to be able to limit the inconsistencies, to have some consistent baseline of ideas and goals.

Whether something is propaganda or not has more to do with the methods and goals, and scale of the communication effort. Like a sustained effort to influence masses of people to do something or change their thinking via a onesided communication, a communication that does not even acknowledge that some opposing ideas exist and actively suppresses them. If it does acknowledge them, it presents them as carricature in order to reject them. It plays into pre-existing biases and weaponizes them, etc.

Yes, inconsistency may or may not indicate propaganda, depending on how big it is, and if there are attempts to hide it, or not acknowledge and discuss it if someone raises the questions.

For example, recently I added a comment under this video https://www.youtube.com/watch?v=0163ne8AQO4 simply stating the fact that this is the old covenant from more than 30 years ago, and there are newer communications that update/contradict it, and linked to the new updated thing https://www.middleeasteye.net/news/hamas-2017-document-full

It was an only comment with actual sourced argument and was deleted almost immediately. So this 50 million USD campaign to spread the "truth" is definitely propaganda. Mass marketed, manipulative, and censuring rational discussion and information that may take away from it's goal of influecing the masses to justify continuing the current war, and avoiding ceasefire/peace. (and the campaign is named "for peace", at that, lol, very Orwellian)

One, fairly obscure letter does not propaganda make. It's more like a manifesto, or whatnot. But yes, if al-qaeda had a sustained campaign specially targetted at western audience, to make it look different from what it's like to locals, to achieve some goals that would benefit the group, then sure, I'd call that propaganda.