Nonsense. The new atheists were never out to 'disprove' god because there's never been a proof for one in the first place. They were out to raise people's consciousness with regard to why they believe what they believe. With the ultimate aim of reducing the influence of institutionalized religion which they saw as harmful.
They failed, which is why a new 'secular religion' of Social Justice sprung up in place of their movement almost overnight. Their atheists turned out to be no better critical thinkers than theists.
Leftist or woke? TNG-era Trek had some ideas that could be maybe considered woke, but it's mostly incompatible. It is explicitly pro-truth, anti-censorship, against judging individuals by their race, but accepted that racial/cultural stereotypes apply in general, and takes a dim view of politically motivated violence. Name any excess of the left at the moment, you could probably find something in the TNG-era shows that criticize it. Somebody already pointed out the 13:50 episode. Leftist, no doubt, that was clearly the intention, but not woke.
It was truly tragic to see, during the rise of Atheism+, the proportion of that community who defined themselves by their skepticism and rationality, but were totally unable to apply those qualities when faced with similar dogma in different clothes.