People (including Catholics) supporting trans rights agree with that.
Of course, most of the Catholic heirarchy and supporters of trans rights disagree on who are men and who are women to start with, but, I mean, the former at least should be familiar with the idea of an entity having the observable physical characteistics of one thing but being something radically different because of its innate essence.
> Catholic teaching is that lying is sinful.
Catholic teaching is that lying consists of objectively false statements told with intent to deceive. (CCC 2482)
> Practicing the Catholic faith by saying "I'm sorry, but I can't 'use your pronouns' because that would be a lie by falsely saying you're a woman when you can't be" will get you reprimanded or fired at most any major US company.
But this is not something that the Catholic faith teaches is lying, even if some Catholics may see it as lying or some other offense against truth. Why?
(1) As Catholic traditionalists and trans rights activists agree, “gender identity” is not the same thing that Catholics see as binary sex. Acknowledging that a persons gender identity is this or that is not a fact claim about the construct of sex, but also
(2) Preferred pronouns are a distinct (though sometimes correlated) issue to gender identity (people with different gender identity can have the same oreferred pronouns, and vice versa), so even if acknowledging the validity of gender identity waa making a claim about sex, and even if such a claim would be false, respecting preferred pronouns isn’t acknowledging gender identity, its just respecting preferred pronouns.
(3) On top of all of the above, the purpose of use of a person's preferred pronouns by a Catholic in a work environment would, presumably, not be convince anyone of some false claim about the subject's sex, and without intent to deceive, it would not be a lie even if its content were an objectively false claim. (Which, for the reasons discussed previously, it is not.)
If you wanted to make an argument against respecting preferred pronouns that was grounded in Catholic doctrine, you would do better to argue that it is adulation (CCC 2480) from the view that transgenderism is inherently wrongful and doing so, lacking the intent to deceive required for lying, is a form of encouragement; OTOH, you could equally argue that failure to do so, in many circumstances, is detraction (CCC 2477) on the same assumption and calumny (also CCC 2477) without it.