Applying for irish passport with british birth certificate?

Hello, I am unsure if i am coming to the right place for help but I am hoping someone here has been in the same circumstance.

I am FTM. I am british and my dad is Irish, I am currently trying to obtain an irish passport. Currently, my british passport has my sex as M and my updated names. However, my birth certificate still has my sex as F and my dead name. I do not have a gender recognition certificate, but I do have a letter from my doctor affirming my intention to remain male for the rest of my life.

I have to use my birth certificate to apply for my irish passport, and I am concerned that the sex on my irish passport will be listed as F rather than M.

I am just wondering, if anyone else has applied for an irish passport using their british birth certificate and passport - did they honour the sex on your british passport?

Cheers