Yes, the the doctrine that no human thought or action is politics-free, is itself politically motivated, and the worldview which subscribes to it is political. It's a doctrine which suits the narratives of all sorts of political activists. Slogans like "if you're not with us you're against us" belong to this doctrine. Every thought you have is political, and so if you're thinking something that doesn't align with our politics, it must be different politics. Different politics is bad and against us.
The doctrine is just something someone made up. It is not justified by rational evidence of any kind.
You are mixing up things: I criticized a worldview and a doctrine, but what is wrong with the doctrine isn't that it claims "every worldview is political", but that "all human thought and action is political".
If it were the former, it would be uncontroversial. I don't disagree with the claim that worldviews are political. The concept of a world view is a set of perspectives and opinions which encompass the human sphere of existence, which has a big political content. (The ideas contained in a worldview are not all political; a worldview needs facts, too, like salt being sodium and chloride, which isn't something voted on in a parliament.)
So, yes, while my worldview necessarily encompasses political topics, I also have thoughts that are rational and unrelated to politics. Or possibly even to a worldview.
The doctrine is just something someone made up. It is not justified by rational evidence of any kind.