@cairobraga : It seems that you cleared up precisely why writing the pronouns in the Bio doesn't avoid that situations.
Let me show you:
Let's suppose somebody talks to someone else about me, and says I'm a baritone. I get notified about such conversation and chip in, clearing up that I'm not a baritone, but a tenor. Then, after that:
1.- If that person still talks about me as a baritone, you and me can agree that would be rude (and pointless!)
2.- If that person just refers to me as a 'singer', it'd be completely alright (no need for that person to specify 'tenor')
I can't recall a situation like (1) in FAWM ever, even in a musical topic such as that (being music the heart of FAWM). So, writing that I'm a tenor (and not a baritone) in my Bio would aim to fix a very unlikely scenario.
But now let's see: would writing that in my Bio aid in avoiding the problem?
If people are not expected to read somebody else's Bio prior to talking about them to others, my Bio reading 'tenor, not baritone' would make no difference. I'd still have to chip in and say I am not a baritone, and the situation would be the same (the other person able to go option 1 or 2). So, it doesn't aid in that situations!
The only other alternative I see where writing 'tenor' in the Bio would fix the issue would be if people are EXPECTED to read other people's Bio prior to talking about them to a third person, and those people being perceived as behaving poorly if otherwise. I'm against that - such is like the 'walking on eggshells' that @ianuarius pointed out, it's very unwelcoming, and just puts a weird incentive for people to look on one's Bio. An incentive not for sincerely knowing about your music and you, but out of social pressure.
I expect all of you in particular to take into account that social pressure can be jarring and not a guide to follow, when you are pressured to do something that doesn't make sense.
But keep in mind, to a person that wants to refer to me as 'baritone' and won't care that I inform I'm a tenor (such as option (1)), such statement of vocal register in my Bio would make no difference at all. That person would do the same regardless of my Bio, since it's a conscious rude behavior. So, you'd be putting social pressure on people to conform, to try to fix a very unlikely problem through a method that actually makes no difference at all.
Now, keep in mind that I was talking about a musical topic. How less likely and overall rude (even just for being off-topic) would be to insist on using different pronouns to the ones a person wants to be referred to in the third person, in a site in which you can be directly addressed without pronouns [such as @user and @user's - which would be akin to saying 'singer' in option (2) ]?.
It seems quite like walking on the street with a hard hat on to avoid getting injured by falling things (like flower pots). It's not that people don't get killed by falling things while walking (150 people die each year just from falling coconuts), it's just that it's very very unlikely, even if using a hard hat is super easy and cheap. Being that such a thing is not lethal (contrary to falling coconuts and flower pots), clearly off-topic, rude, and quite against the rules for many other things than misusing pronouns, this makes no actual difference. The situation would be settled quite easily.
Gender doesn't make any difference in what music you can make - people of any gender can make any music. Now, people of different sexes have different average vocal registers and timbres, but that's not about gender at all - don't confuse gender and sex.
Differentiating people in a musical context by non-musical things like who informs their pronouns in their bio or not, who use those pronouns or not, and who is an ally or not... is to differentiate between people according to characteristics that don't make a difference in their music, and such is precisely what discrimination is.
Now, you seem to be supposing all people agree in some basic grounds about the concept of gender, and that is not the case. Even more, people can have good reasons to disagree with that.
For example, gender can be seen as subjective (say 'in the eye of the beholder'): For example, we adscribe the gender female to the Venus de Milo... when it's just a piece of marble, perhaps not even sculpted by a female. It doesn't have a sex, of course. What entity is the 'gender' applied to is our concept of what it is depicting. That idea has a gender, and everyone can have different ideas, hence the idea of a person can have different genders according to whom we ask, and maybe all of them don't have to be forced to coincide with the subjective view a person has about oneself. Perhaps I'm wrong in doing so, but I expect you folks more than anyone else to be aware that people can be confused about the gender they think they are.
The same goes for historical figures whom we don't have their own statement about which gender were they. We don't have a problem saying Tutankhamun was a 'he', because we perceive what we know about Tutanhamun as matching what we expect of a male, and it's alright. You people, more than anyone else, can attest that you can't deduce the gender or pronouns of a person out
Another example is that maybe gender is not part of who you are. It may be something you like, or agree with, of course, but it may not be part of you. If somebody gets something changed and the person afterwards is identified as the same somebody (not an entirely different person), then such a something that changed was not part of that person after all. If it was part of the person, removing it would have destroyed that person.
If you remove the head of a person and replace it with another head, you can see that -afterwards- it's not the same person, if you could make the operation. Same as when you cut your hair. One's hair is not part of who you are, since you identify yourself as the same person prior and after the haircut.
In that way, somebody can attest to having no gender. Not that 'a-gender' would be a gender, but a person not having a gender.
Besides it all, the uncritical stance about pronouns make for all kinds of problems, such as a person attesting their pronouns to be "I/my". For it to be worth taking into account, it needs to make sense - at least, to be coherent: if one is to accept any pronouns, those are possible, so you'd be talking about a third person as "I", for a funny example.