"Normal" is actually a difficult concept for me. I grew up in an aging family back in the 1950's & 60's. The values I was taught were those of small town America in the late 19th & early 20th centuries. There wasn't much flexibility there. Unfortunately, although I didn't learn what it was all about until the beginning of my 6th decade, I was either born transgender or became transgender very early in life.
Somehow, I don't know how, I learned very early on that being what I now call: "transgender" was something I must NEVER talk about. And so I kept it a closely guarded secret for many decades. And, over the years, it has eaten me alive from the inside out.
The complicated part of this is that, try as I might, I still basically hold to those late 19th century & early 20th century small town values. They are the gauge by which I measure what is & is not normal. I can say, intellectually, that I no longer adhere to these values, & I don't. But deep down, they are still there, working their "magic".
So, what is normal? I don't really know. But I do know that the person I am does not, in any way, adhere to the concept of normal I have tucked away in my mind based on the upbringing I had so any years ago. And there is a sense in which the opposition of these two conditions probably lies at the base of much of the mental health problems I struggle with today.