In Tenet, the people of the future suffer because of the climate change of the people of the present. Therefore, the people of the future use things (weapons...) that travel back in time in order to kill the people of the present.
Here the question of the grandfather paradox arises: Do you die if you travel back in time and kill your grandfather or other ancestors? In Tenet, it is clearly stated that the people of the future think that the answer to this question is no - they think they can kill their ancestors without dying. Thus people of the future see no temporal paradox, instead, they simply believe changing their past (by killing the whole of humankind) does not change their present. At the same time, the people of the future believe that changing the climate of their past does make a change in their present. Isn`t this a clear contradiction?
My question is about this contradiction in the view of the people of the future, not about the logical inconsistencies of the grandfather paradox itself. Meaning: It does not matter what the grandfather paradox says about changes in the past but just what people of the future think that changes in their past mean. The assumptions of the people of the future are the ground of the whole story because they are the reason why the war starts.
Edit: My question is based on linear thinking where time goes forward, i.e. the cause precedes the effect. In linear time we can ask things like "do they think changing the past changes their present?". But the machine the people of the future breaks this linear time flow and with this the contradiction described in my question vanishes. (I suggested this edit to the answer but it was not approved for some reason.)