Saying the Imperium would automatically burn troons at the stake is frankly silly when juvenat and other body modifications are readily available if you have the money and means.
The Imperium is not unified, so it's specifically the Ecclesiarchy. You know the Evil Space Catholics x1000. The Ecclesiarchy do have an awareness of Chaos, Chaos acts upon the individuals indulging in their freedoms (except Nurgle, he's kinda weird). The solution then is to not allow people freedom, not to allow them free expression, or much individuality. If you're entire day exists out of working, sleeping, praying and a few minutes to eat (generally shitty food) then you don't have time to join a Khorne speed metal band or Slaanishi drug den. There is admittedly some variety from world to world, but I'd say any work with a notable Ecclesiarchy presence the stake option is very likely end when a priest sees some some kind of Ogryn in a dress telling people to respect it's gender pronoun.
Also there is rarely modification done in the Imperium for aesthetic reasons, outside of the Mechanicus (and arguable even there how focussed they are on looks). The reason for augmentation and modification is largely functional. Genetically enhanced soldiers are modified for war, if a citizen loses an arm or a leg a cheap and dirty mechanical replacement is slapped on so that they can continue working. Rejuvenation technology would also fall under the functional, since the goal is extending life and presumably quality of life.
The best possible chance would be for the nobility to maybe get away with this, since they are offered more freedom and less supervision but even then they'll like get a visit from the Inquisition and at that point it's a coin flip.
People forget that 40K isn't really a nice place to be and that's fine, it totally can be a horrible, intolerant place and it's fine to want to engage in that because it is all fictional. Not all entertainment has to have the same core values, or present some kind of moral lesson, or even invoke the same feelings. I watch dumb 80s action movies because it's exciting, I watch horror movies because I want to be scared or be exposed to things that creep me out or make me uncomfortable, I watch comedies because I want to laugh (but recent years comedy has failed to do that...). There really is no reason fiction should always be representative of modern norms and morality, in fact fiction is best (in my opinion) if it allows you to experience things very much outside of what you can experience yourself, different worlds, different ideas etc.
Gav ‘fucktard SJW squatkiller’ Thorpe. The pronouns in question were ve/vis/ver and the novel was Imperator: Wrath of the Omnissiah.
Old lore vs new lore. Or maybe rather interjecting modern day into a non-modern day setting. It the equivalent to having a story set in medieval Europe and having a character greet another character with "Yo dog what ups?".
But it is admittedly difficult to say with the Mechanicus, they're all over the place lore wise, sometimes they're legitimately technologically illiterate working with barely understood technology, other times they're hyper advance, constantly experimenting and innovating.
Getting a good grasp on their core beliefs is really difficult because they seemingly don't have any (all up to the author then), and unlike other Imperial organisation there isn't really much of a real world analogue to draw on. The Ecclesiarchy are evil space Catholics, the Adminstratum are hyper incompetent bureaucrats, etc. But sadly there isn't a real-world analogue to the toaster enthusiastic.
