In my last game, a culture dominated my empire to a large extent. Accordingly, a war was no longer possible, as I lost 45 war support every round, since my territories followed the culture of the opposing empire. Is it not possible to remove the influence of culture from the calculation of the state of war, or at least to weaken it?

You can weaker opponents influence by 3 ways:

1) Improve your influence by picking aesthetic culture and using their affinity 

2) Pick the isolationism in international trade civic

3) Pick world homeland in foreign customs civic