What a rich, provocative question!
First - "I am a feminist" is shorthand for " I believe women and men should have equal civil rights or dignity or..." or any number of other belief statements.
Actually, I think if I hear you say "I am a feminist" I still do not know anything about you.
There are many different beliefs that someone has labeled "feminist." Some self proclaimed feminists believe in equal rights and dignity - probably most. Some believe all men are bad (probably a minority).
I sometimes say I am "pro-feminist." I want to label my beliefs, not my Identity.
As to what it has to do with being trans.... My first inkling there was a problem in my gender identity was when I started paying attention to all the ways men as a group are socialized to mistreat each other, and women and children, by being aggressive, competitive, domineering, inflexible, sexist, homophobic, emotionally constricted and so on. I did not want to be a man, if that is what being a man was.
Certainly, I was able to find other definitions of manhood, and examples of gently strong, compassionate, aware men. I appreciate the trans-men on this site helping me remember the positives of being a man I forget sometimes - because I want out of it for myself.
I have spent much of my career trying to help men be the second kind of man. It distracted me from realizing that it was not that I did not want to be a man; I do not feel inside I am a man. Birth assignment notwithstanding.
On the other hand, I had to face my own internalized prejudices against "femininity." (I really appreciated Whipping Girl by Julia Serranno to see this more clearly) Ironically, She points out even self-described feminists sometimes hate femininity. I had to learn to accept my own femininity to accept myself. To me, that is part of believing in equal rights for all gender orientation/identity choices. We have to reclaim the dignity of femininity.
On the other hand, I do see chivalry as problematic. Many of the laws restricting women's access to equal employment were originally passed to "protect" women. Goddess protect us from "benevolent" patriarchal protection! No one but me can really decide what is best for me.
(Almost) every fortress eventually becomes a prison.
I also believe that the binary gender polarized social stereotyped structures, socialization and social behaviors that are detrimental to women (and anyone who does not fit the stereotypes) are also detrimental to conventional men. A man who steps outside of the stereotype - by not being strong, rich, dominant, confident and so on, is given grief. A feminine man is hated and scorned by many. But the men who stay within the stereotype are less able to be fully human - less able to feel and express all their feelings, less able to ask for needed help, less able to even know they are handicapped and unhappy. Many, maybe most men lead lives of quiet, confused desperation. They pay the price of "male privilege" but never experience the illusory "benefits" of being a powerful patriarch. Even powerful men are frequently miserable but unable to recognize of fix their basic unhappiness. Being socialized male is emotionally handicapping. ( I know I am generalizing a lot, but notwithstanding the exceptions, there is truth in what I am saying. In part, I emphasize that many men do not completely live within the stereotype, and are therefor able to be more fully human.)
I believe feminism has contributed greatly to human society and to my personal experience, including my ability to accept my inconsistent-with-my-body female identity.
