I just don't think the atheistic element is as prominent as all the other elements. If I remember correctly, the campaign that did a lot of damage to the religious houses and establishments was the Destruction of the Four Olds, and that took out a lot of cultural/philosophical stuff as well.
First, you're drawing artificial academic lines between culture, philosophy, and religion where there aren't any. Most Asian countries have never had the sort of religiously divisive struggle like the European Reformation or the Rational Movement. It really doesn't make any sense to say something affected religion less than cultural/philosophical because they are intimately connected. To give an example, much of traditional chinese medicine (acupuncture, cupping, herbal medicine) was denounced during CR as backwards superstition. Chinese internal medicine theory is based on the balance of elements (metal, fire, earth, water, wood) within the body. This theory also extends beyond merely the human physiological body, and is the driving principle behind Fengshui (rearrangement of living spaces for harmonious living, including health and material success), Taoist fortune-telling (I-Ching), Traditional Chinese Cooking (balancing 5 flavors of sour, spicy, bitter, sweet, salty), to Chinese theory of aesthetics in art, poetry, and music, and even Chinese martial arts (like Taiji or Hsing-I). So when the red guards come and beat up a Taoist Qigong master who practices acupuncture and healing in a rural community, is it about religion, or culture, or philosophy? Or maybe it's the case that such divisions is meaningless.
Second, the impact of the CR extends before and after the actual events and resulted in decades of harsh crackdowns on minority ethnic/religious groups like the Muslim Uyghurs. Towards the end, there was so much chaos that the Communist politburo was afraid that these groups would rise up and rebel (many of them started to). The crackdown that ensued included the banning of all religious symbols and displays, and the outlawing of speaking minority languages like Uyghur and Tibetan. There were other groups too, but I bring these two up because they're most widely known.
BTW, lest someone get the wrong idea, Mao did a lot of good things too, like banning foot-binding, eliminating arranged marriages (which was usually a young woman to a much older man), virtual serfdom of many chinese peasants, and improving the overall quality of life of the majority of chinese people.
I said it was clumsy, not technically incorrect. Using a generic descriptor gives one the image of the entire class of people — mechanics, Muslims, Atheists, writers. Muslim extremists or Muslim terrorists gives one the image of the perpetrators and not the entire class.
Truth is still truth, even if it's uncomfortable, inconvenient, or politically incorrect. Again, general ignorance should not be a hindrance of stating things as they are. Would you feel more comfortable with calling Mao an Militant or Extreme Atheist?