Many do not really know the term culture war. Many do not understand culture at all, and many of these are Marxists. Don't feel bad, actually very few conservatives or people on the right understand it, either. But it is a term most often used by Marxists, and it was invented where Marxists thrived in Germany and Prussia in the late 1800's.
Marxists used the term "culture war" (aka. kulturkampf) as a political term, in order to describe the type of propaganda it would take to create the kind of lasting unity in Prussia and Germany, so that they could unite their nation. None of this had to do with what culture really is in reality– or what culture means to a free society. That wasn't their concern.
So, to those of us who live in free societies which are grounded in civilizational principles, which in our case means it is founded in Judeo-Christian values (giving us freedom), it means that culture is a voluntarily-built part of the fabric of society. It's not something that gets imposed upon us in a top-down system of authoritarianism. This kind of western culture (a culture of freedom) gives it robustness and resilience, but it also means that anyone can participate in it. So, it is a classless society, in terms of culture. But this isn't true in Marxism. In addition, sadly, this robust openness in free societies also makes it more vulnerable to attack by Marxist cultural deconstructionists, or competing faiths such as Islam.
So, the culture war is a product of Marxism, which serves to create a middle-ground in which Marxists view the culture as dangerous, and Christians view it as a product of joy and social cohesion. Something for us all to participate in and have a voice.
This joy– this freedom– is not a part of culture for the left. They aren't allowed to say what they want. Instead of this place of play and enjoyment, they live in a state of obeisance to the mob and in a state of obedience or fear to the system. This system of fear is about creating an ordered society for them that they can exist within. This is because the Judeo-Christian state of order (self-policing of speech) is not something they are taught, and eventually they lose the ability to do it. It takes self-discipline (based upon divine purpose) to do that. Since they do not affirm God's existence they have no divine purpose. So the state provides this order for them.
That is why culture and its purpose is VERY different for the Marxist. It is a source for propagandistic messaging for the left and the right. They cannot simply enjoy storytelling. They must make themselves, as a belief system, look good and therefore feel good through such propaganda. Otherwise, why are they doing it?