They forgot the golden rule of tv, make a good show first.
But the show was pretty much about identity for most of its first ten series, not to mention that you could say that there is an inherent aspect of transness to the character of the Doctor (especially their experience with other characters familiar with past incarnations of the Doctor). The show plays a lot with gender, especially around the timelords.
Heck, even on a purely literal textual level the show is extremely LGBTQ from the start. Captain Jack Harkness is openly bisexual (or pansexual) and flirts with the (male presenting) Doctor who is clearly intrigued. The "love triangle" subplots largely play out more as depictions of polyromantic relationships rather than sources for drama. Even without featuring any clearly trans characters, the show is fundamentally queer if you even barely scratch the surface of it.
I guess if you want to consider the show overly "woke", that started as early as when Martha Jones became a companion because her race became relevant to the plot. The only thing that changed with the newer series is that the writing IMO got sloppier.
That's all percectly reasonable but I don't see how this has anything to do with the discussion related to the article, given that the new Doctor Who show started in 2010, Netflix only started doing its own productions in 2013 and most complaints about "too much politics" tend to be about media produced in the mid-2010s onwards (the Ghostbusters reboot was released in 2016).
I’m really not a prude, I hope, but I prefer to keep my intriguing and backstabbing separate from my softcore pornography.
When telling a story on TV, you often want to cut the story to the bone such that it can be understood quickly and entertain without confusing the viewer with side tangents that aren't central to the story. If a non-story-essential element is too prominent then the viewer might feel it's boring