So, there are actually 3 components going on.

Gender Identity,

Gender Expression,

Biological Sex.

So for example, I am a woman, who wore pants yesterday. I also don’t wear makeup, and I chose to wear men’s deoderent. That is something that effects my gender expression. That is gender expression. That being said, I am clearly a woman. I feel like a woman, I identify as a woman. You can put me in the most male clothes you possibly can, I will still be a woman. You could attach a penis to me, sexually alter me, and I will still be a woman, because that is my gender identity. I identify as a woman. But the ‘stylized reptition of acts’ is gender expression. Yes if I wear pants one day, I will still feel that I am a woman. Putting me in clothes and making me play dress up will not change my gender identity. I don't kow what would change my gender identity, but being told I am a man over and over again, being forced to act and live as a man will not change the fact that I see myself as a woman.

Now my biological sex is female, so it's generally assumed okay that I call myself a woman and live as a woman. I can wear pants, and even cut my hair short and because of my biology, no one disputes my gender identity. So therefore I am cis gender.

However, If you pick me up as a person, and transplant me into a biological male body, and still be me, I think I would still in my heart feel like a woman. I think this is what happens to trans people.

Trans women can live as women, and one day decide to wear pants, cut their hair short, work in male dominated fields, play football, just as any woman can, that doesn't change her gender identity anymore than it changes mine. Even though all those things are associated with being male, they are gender expression, they are not gender identity.

Gender Identity isn’t a ‘stylized reptition of acts’ it is who a person actually is. "Stylized repition of acts" is gender expression. I met a little boy whose favorite color was pink, he was still a little boy, but he likes pink. That doesn’t make him a girl, even though that’s a preference associated with being a girl. He’s still a little boy, he just likes pink. I have no idea what this little boy’s genetallia or biological sex are, I don’t think it’s appropriate to ask little boys such quesitions, or wonder about them.

I could even go and cross dress as a man, even live as a man. That would be changing my gender expression, but since I know that I am a woman, it would not change my gender identity. Cross dressing and living as a man would not make me trans, because my gender identity is female, trans men identify as men even though their biological sex is female.

I suggest you consider learning about the two different things if you're going to analyze this typic, it might help a lot. Cis people, we often haven't had to see and examine the difference between gender expression, gender identity, and biological sex, and it can be hard for us to understand how they are different and which ones determens trans/cis, since for us they are messhed together. Our privledge prevents us from seeing having to examine this.