When we say that they "present" as a woman, we're explicitly referring to their persona or identity rather than a biological fact. In other words, you've already adopted their narrative.
This reminds me of the difference between the verb to be in Spanish. There are two of them; "ser" and "estar".
Estar deals with the condition or the “how” aspect of an object or person. It is used to depict the mood or the condition of an object or person. Ser relates to the location of an item as well as a person or a group of people.
Ser is used to refer to the physical aspect and the “what” of an object or person. Ser is used to define physical characteristics such as colour, texture and so on if the verb is directed to an object. It also depicts personality and character as, gender, race and nationality. Ser is used to relate to the identity of an object or a human being. In referring to “what” an apple is, the verb ser is used.
The debate becomes much more convoluted when we ignore these distinctions because one side is presenting a gender using one idea while the other is using the other. Although, it also appears that those who "present" as a woman are conflating the two as well. They have a group identity, yet they also indulge in stereotypes, fixed mannerisms, etc. They insist not only that one must view them a certain way, but that these views must conform to a certain set of norms, customs, styles, etc.
With regards to your analogy, there isn't enough information to be of much use due to the fact that most people do accept and patronize those who present themselves as plumbers, doctors, and scientists without really going into any depth to ascertain if their credentials are legitimate.
We already have some states presenting documents that offer more than a few options for gender/sex to establish and legitimize them.
I've gone to see one doctor after another who had a wall of diplomas from reputable universities, and yet I will never go back to any of them ever again because they're clueless how to treat people who are sick with anything other than tests that are predominantly inconclusive, surgeries, and prescribing petrochemicals that they know almost nothing about.
