I think the "culture" relation is more comparable to if a male were to portray feminine characteristics. Nothing wrong with that, ones just a feminine man, however, this doesn't mean that the man can become a literal women because of these traits.
Here is the point of my original post that I want to emphasize: People on the conservative side of this want to stress the fact that they are on the side simply using logic, talking about objective facts, that they are right on biological grounds, etc. However, every time this framing is used, that a trans woman is a man claiming to be a "literal" woman, a man "pretending" to "really" be a woman, and so on, this is a distortion and an attempt to load the language in a way that prevents the issue from being discussed in clear terms.
Trans women (for example) are not claiming to "really" be "literal" women, or at least do not need to. All they need to request is for the concession in the use of everyday language. Using she/her pronouns, and even using the term "woman," does not need to imply anything about their biology, or the gender they were born as - "woman" can here simply be used as a shorthand for "trans woman." The real conservative side of this is not that trans women are "not really women" or "not literally women" because this is just a loaded use of language to state what would otherwise be completely obvious, and something on which neither side disagrees. The reason trans people do not want to concede that use of language is not because they are deluded about biology, but because it violates the social norm that "woman" can be used as an acceptable shorthand for "trans woman."
In fact, the conservative side is that men taking on social roles previously reserved for women, and asking for this concession in the use of language, is somehow a degenerate or anti-social behavior which should be culturally penalized and discouraged or at least marginalized through indirect means. The need to deflect from their essential position (that deviation from gender norms should actively be culturally penalized) by using strawmen about biology, as well as wedge issues like bathrooms and women's sports, is because that fundamental position would be unpopular if advocated directly, but you can move people to eventually agree with it through the use of framing and wedge issues to gradually move their sentiments against trans people.
Bu this is only because society has not reached a point in which race, age and species are intimate aspects of self-expression. Are you suggesting that, were people to reach that stage, it would be correct to then base the identity of people purely on how they feel?
I don't think this would be acceptable in the case of age or species because of the mentioned links they have to autonomy, e.g. the obvious ethical issues that would arise from allowing adults to identify as children or vice versa. In the case of race, it could be the case that when the nation-state model has dissolved, and free movement has developed to the point that ethnicity is untethered from territory, the cultural aspect of ethnicity totally dominates the biological aspect.
I don't think the question here is "would I refer to a trans man as a man", for you would hardly find anyone who wouldn't on the simple grounds of common courtesy, but the question is are they actual men. Just as how one can cosplay for the day and "adopt" a new identity, that costume does not define the essence of your character.
The question is what you mean by "actual men" as I described the problems I have with this above. The reason I believe trans people have a problem with the statement that they are "not really men" is not that they disagree about the biology, but that it violates the linguistic norms which would make them feel included.