PickingOakum
From what I have read the profile of late transitioning males is that they are generally the autogynephiles, the fetishist cross-dressers.
They are usually married, often more than once. And have fathered children, often have more than one family.
The "affinity" with womanhood comes from the cross dressing. It's entirely sexual and involves heavy porn use. It's frequently accompanied by feelings of guilt and shame. Memories of masturbating into family members' under wear , etc.
Secrecy and furtiveness are a part of it. If they 'come out ', that is often accompanied by a divorce. Coming out also, occasionally, seems lower the drive. As secrecy diminishes, so does the excitement.
However forcing people to use pronouns and treat them as a woman, is arousing.
It can also get rather bizarre when the desire to subsume womanhood directs self at biological functions like periods, childbirth, breastfeeding, etc. Taking an unhealthy interest in it, disguised as empathy or sympathy. Many videos on YouTube of AGP individuals claiming they have periods, using Tampax or attempting to breastfeed/produce milk.
So, in terms of your theory: I think they would be drawn towards things that are particularly for women, not avoid them. But because the interest is sexual, there is no understanding or appreciation of the material reality.
And as for joining typically male dominated jobs or sports, I think this could be an attempt to counter their hidden life of cross dressing. Because it does become a huge compulsion. And part of it is to be humiliated, cissification, etc. Presumably when that is accompanied by huge feelings of guilt and shame, there is a need to counteract it.