This is a fantastic question. You are wonderful for your level of consideration given a perplexing situation here.
The Problem: I used to be Emily. It's over 25 years later, and this thing just doesn't really go away.
At 14 you already knew at 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13, every day. Yes, Emily thinks about this at least as often as any teenage boy or girl thinks about sex or eating. If it's real, she thinks about it more than either you or your girlfriend and you are both extremely important people in her life.
It is intertwined with who you are, and, guess what the real curse is? Visions of alternate lives aside, it really shows up whenever you want to have a relationship with someone. So what you can hide all this in your normal life, you can't when you have a relationship! Because the other person can taste it. All your instincts are "backwards", and people hate you for it. It doesn't make any sense, but you can't escape it. Hours into years and reunions tick by and it's still there.
You're guilty whether you come out or not. People smell it. If you line a class up on a wall we all know that Jeff is more of a man than Charlie, Joe's weird, and Jeremy wouldn't know masculinity if it hit him in the face. Worse, people smell it on strangers 5 seconds in. It's instinctual.
And all the alpha males already smell it on Emily. She's locker-slamming bully bait. Emily doesn't have a safe alternative here. Transitioning isn't safe, it's just sometimes less dangerous. It replaces some of that 41%+ suicide rate with temporarily higher risks in other areas then probably lower ones later. Women who have been sexually assaulted, an acknowledged nightmare tragedy, have a 24% suicide rate. Meanwhile, this thing which Emily has a hard time explaining to people is probably the #1 reason she might die, likely to take her life long before any cancer or accident.
Sexual assault rates are worse, even for the racially privileged:
- white cis male: ~6% (4-15%)
- white cis female: ~20-25%
- white trans male (FtM): 55%
- white trans female (MtF): 68%
Your girlfriend's stance is dangerous for Emily, especially if Emily has access to a gun. If you do, hide it. Males succeed at suicide at far higher rates than females mostly due to readily available access to guns (often from former military service). This is a thing you need to be aware of now since reactions like your girlfriend's, combined with local bullying and gaslighting, are exactly why people with gender dysphoria kill themselves.
Acknowledgement, allies, and transition: The grand blessing of being able to actually be the gender you are inside is that your instincts come back. Instincts are what let you read meanings that are so potent they are unspoken. They tell you when there's going to be a fight, why, and how to handle a particular fight. They let you avoid and settle disagreements. Instincts keep you alive. We pretend we've grown past that, but no, normal privileged people have -- white males can fight "with honor" and talk to a cop without getting shot. Minorities and LGBT people are shot, knifed beaten to death every day.
Emily is that, whether she transitions or not. People, men and women, will call her a fag across the street, regardless of how she changes her life. They will smell that something isn't right with her, they will single her out, and punish her for it whether she alters her appearance or not. And chances are no "justice" would ever result. The conviction list for people who beat up on trans people is extremely short. The number of people who bully, marginalize, gaslight, mock, disparage, attack, assault, and outright murder trans or gender dysphoric people is a significant portion of society. Sure, aggressive alphas are a small fraction, 5-15%? but they vastly outnumber trans people at 0.6% and prove themselves by picking the seemingly weak, the outliers. Emily has outlier branded on her forehead whether she wears a dress or not.
Your girlfriend's world has a lot more safety, and many more knowns in her own life than Emily does. Emily is a minor. Emily is the underdog here, and she carries a horrible curse she never chose. She just woke up with it years ago. Yes, parts of it are indeed wondrous, but much of it is unfortunately difficult. Any God there is made her this way.
I grew up around fundamentalists. Jesus ate with thieves, reviled tax collectors, and prostitutes. At worst for kindness and compassion, Jesus would surely break bread with Emily, listen to her, understand her. Given that he preached turning the other cheek, and is shown with beatific eyes, and a peaceful demeanor, clad in a flowing tunic -- dude, future unwanted beard or not, Emily probably looks and acts more like he did than most people. Jesus preaches that you know a person by their actions. How is wearing a dress, caring, and expressing heartfelt emotions in an undudely way a sin when half the people on the planet do it every second of the day?
Gender makes up <2% of our physical body mass. Good gravy, for someone who really substantially wants the other side, is it really worth making them feel like trash over some hidden piece that isn't even public?
Going forward: Emily has different thoughts. Ask her the stories. I wish you all well, and that she, you, and your girlfriend have the chance to meet others who see the world her way. There are some amazing discoveries in there which not many people understand, and once you see them, it frees you in your own life and allows you to do and experience life in a different way, even without changing how you look or behave. It relates to the same deep emotions that are why we fall in love, experience beauty, strength, possibility and wonder. There are awesome things ahead. Transitioning is better younger. Given her age at 14 Emily will be noticeably anxious about irreversible change of puberty. Please, listen. It's a curse because most people don't accept it, but that doesn't mean it doesn't have many unusual and amazing treasures. The important thing to do is see what is there and let those hidden things come out. Chances are the demons and the sharp things she's been tripping on in her subconscious will change in the light -- hey! Turns out that thing that's been slaughtering my shins at night in the dark is really a... harpoon gun? Wait, this creepy basement was really a Bat Cave the whole time? Woa! No wonder it was so dangerous.
I can't describe the moment of how powerful it is to feel the change, but Hollywood already has in many movies where the clumsy nobody turns into a superhero. You can't be a superhero in life, but you can be a woman*.
For some of us, it's basically same thing anyway. Even if, in practice, it means being a second class citizen who can be interrupted, belittled, underpaid, hit on, and pestered by men (and other women) in different ways every new day. Yay?
(*)with footnotes and sans reproduction, but done well, you really can convince most other people and have hardly anyone know, especially if you start young. At the end of the day it's hormones, acting, and making the best choices for how to deal with the particular pile of crap life dumped on your driveway. How is that evil?