There are numerous programmes on the lives of trans people covering a variety of topics (relationships, culture, health), some news stories reporting facts (mainly people and organisations getting 'cancelled' for being anti-trans) and articles based on public comments from well known people regretting decisions.
I assume you are referring to the controversy around a single article by a single journalist [1]. A journalist who previously wrote a sympathetic history of trans people in the modelling industry... for the BBC[2].
Out of curiosity, I tried to find any other evidence. All other descriptions of this anti-trans agenda ultimately just reference this single article e.g. [3]. One 'article' becomes 'articles' and then slips into being an 'agenda'[4]. I found one other reference - an article about an internal meeting which some attendees complained about, but that wasn't even public facing and was only called because of that single article [5]. (There were also some vague references to two individual news stories, which were considered by some to not be balanced - there are complaints like this about news coverage from either side of any argument every single week on the programme Feedback.)
If the BBC is trying to promote an anti-trans agenda across their massive output involving tens of thousands of people, they are doing a spectacularly bad job of it.
I get fed up of people bashing the BBC over individual incidents - it just feeds into the right wing narrative that it needs to be de-funded [6]. Be careful what you wish for, privately owned media tends not to be great for marginalised groups...
[1] https://www.bbc.com/news/entertainment-arts-59074096
[2] https://www.bbc.com/news/uk-england-49578690
[3] http://www.ilga-europe.org/sites/default/files/2022/united_k...
[4] https://www.gaytimes.co.uk/life/drag-race-uks-bimini-calls-o...
[5] https://www.pinknews.co.uk/2021/11/11/bbc-trans-lgbt-staff-s...
[6] https://www.gaystarnews.com/article/mps-and-trans-campaigner...
Before that, staff were told that attending Pride was no longer allowed.
This week the BBC Woman’s Hour platformed Maya Forstater as a feminist hero. They didn't critically mention the real reason she was dismissed from her contract was for handing out leaflets at work that said trans people are a danger to children.
(I don't work for the BBC and internal matters are somewhat opaque to the outside world, but even the Pride issue seems to have been some poor interpretation of a brand new guideline by someone internally that was spun into a bigger story and dealt with within a few days - https://www.bbc.com/news/entertainment-arts-54749024)
I'm still struggling to see the evidence for a war.
This is the BBC doing its job admirably, presenting different points of view and perspectives, to educate and inform the reader in as neutral a manner as is possible in journalism.
I mean, the BBC is very happy to turn refugees drowning in the English sea into entertainment. And is currently waging a war on trans people.
Sure, the BBC is less bad than RT, but not pumping out doctored footage or blatant antisemitism is a very, very low bar.