user centered design - Using genders in physiologically oriented UCD

I've this problem: as a policy, we usually strive to leave out gender considerations if possible. If not possible, we use a wide range of genders . Not as extreme as Facebook, but something more rational around physiological genres (Male, Female) and commonly accepted LGBT concept (Lesbian, Gay, Bisexual, Transexual).

Problem is that now we need genres based on physiological aspects due to an algorithm we're using were physiology is the key (and obviously, a woman is not physiologically the same as a man, despite the chosen gender identity).

Our closest solution is to include male/female and a short message explaining the reasons for this. However, this approach deals with genitalia, and transexuals were born as one sex and now are another sex, which means that physiological aspects are mixed.

So question is: is there an accepted way to deal with this kind of problem without leaving out anyone, yet covering all bases?

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EDIT: this is for a healthcare app dashboard The thing is this app uses an algorithm to define certain specific vital stats that are different for males and females BUT transgender uses hormones that modifies some of these vitals. We don't know until at least a V2 if the app will have transgender users, so my question goes around some wording or conceptual approach to deal with such sensitive information. Note that We're ok with just using male, female, other ** and if **other is chosen, explain the Other option and why we ask for that, but I was wondering if there's a better way

EDIT 2: I completely forgot about this question. For those interested, we went with "Other", and when this option is selected, a dialog with a sensible message pops up asking user to specify what they mean, and also requests information on treatment based on their answer. Thank you Zoe, Ivonne and all those who commented, you were really helpful. Sorry for being this late

Answer

If this is a healthcare app, there is at least two very different ways to tackle the issue, based on the diversion of mental health and physical health. If this is a non-healthcare app, asking for this kind of information is quite invasive.

Hoping this is a healthcare app, to give a definitive answer I would need more information on use cases, but based on your question:

1. 
   

   If you need users to choose what gender/sex they were assigned at birth, before the possible transition to a gender they identify with now, the term you need is just that, "gender assigned at birth". This will answer to "which set of visible genitalia they were born with". NB: sex assignment at birth is often a faulty method that doesn't spot people born with the mosaic sex, one set of hidden genitalia or else https://en.wikipedia.org/wiki/Sex_assignment

   
   



2. 
   

   If you need users to identify their current set of genitalia, I think you could just be blunt and ask them to choose from four options:

   
   
   
   
   • female genitalia
   
   
   • male genitalia
   
   
   • female and male genitalia
   
   
   • mosaic genitalia.
   
   
   
   

Important thing here would be to add a memo tooltip where you would explain why the service needs such private information. Another important thing would be to never mix language for gender (social construct and compound of behavior) and sets of genitalia, because these are two completely different things.

3. 
   

   Lesbian, Gay and Bisexual is not a gender, it's a sexual orientation.

   
   


4. 
   

   Some other genders: agender, bigender, queer.

   
   

Upd: adding a classification for clarity: