You mentioned mental health organizations.
It may be just me. But let me tell you Pshychiatry and psychology is ever evolving subject. It has no absolute.
All fields of study are evolving. Additional research, education and experiences mold these evolving interpretations. As has been pointed out, homosexuality exists in the animal kingdom, so it is not "against nature".
I find it illogical that there are people with fantastical beliefs of an illiterate man accurately delivering the final words of God by listening to an angel in a far away desert 1400 years ago. Just becuase there are a billion people today with those beliefs doesn't make it true, logical or disease-free. I'm sure you don't agree, but an unbiased person can easily interpret that mindset as illogical ideas of the mind. As you said "..... mental disease definition is based on how many sick people themselves are defining it."
In my country there are many times more gays than Muslims, so if we are basing what is "normal" or "accepted" by what the majority believes those definitions to be, homosexuals win out over Muslims.