My (M31) new girlfriend (F29) doesn’t want me to keep this friendship

FYI have used AI to clean my terrible writing up but all the details are accurate.

I (31M) have been dating my girlfriend "Emma" (29F) for about 6 weeks. We are long distance and I was supposed to be flying to see her tomorrow, but right now we're not speaking and I honestly don't know where we stand.

The situation revolves around a friend I'll call "Rachel."
I've known Rachel for about a year. We've hung out one-on-one a handful of times. Before I met my girlfriend there was one occasion where we were physically affectionate (cuddling and holding hands), but there was never any dating, relationship, romantic discussion, kissing, sex, or anything like that. We explicitly talked multiple times about being friends and that's how I viewed it.

There's another layer to this. My dog bit Rachel in the face last year and left her with a permanent scar. I feel a lot of guilt about that.

When my girlfriend found out about Rachel, she was very uncomfortable with the friendship. During an emotional conversation I offered to cut Rachel off completely. Looking back, I think I offered that because I was trying to reassure my girlfriend rather than because I had actually thought it through.

Over the last few weeks I've reflected on it a lot and realised that I don't actually feel comfortable cutting Rachel off completely.
To be clear:

I don't intend to see her one-on-one anymore.

I would happily reinforce that we are just friends.

I would be transparent about any contact.

I don't think there is any romantic threat there.

But I don't feel comfortable telling someone who hasn't actually done anything wrong that we can never speak again.

Part of that is probably guilt over the dog bite situation. Part of it is that I genuinely think it's unfair. And part of it is that I think I'd grow resentful if I agreed to something I don't believe in.

The complication is that recently my girlfriend had her own situation involving a male friend I'll call "Mark."
Unlike Rachel, I genuinely don't care that Mark is in her life. I never asked her to cut him off and I don't feel threatened by the friendship itself.

After that situation happened, I started thinking more deeply about friendships and boundaries in general and realised that my original promise to cut Rachel off didn't actually align with my values.

I told my girlfriend this.

She sees it very differently.

From her perspective:

Rachel is obviously more than a friend.

I'm choosing Rachel over the relationship.

The fact that I changed my mind proves I'm inconsistent.

The fact that I won't cut Rachel off means I'm prioritising Rachel over her feelings.

From my perspective:
This isn't about choosing Rachel.

It's about not feeling comfortable cutting off a friendship completely when I don't think it's warranted.

If Rachel disappeared tomorrow, I'd still feel the same way about the principle.

The argument escalated massively.
My girlfriend told me things like:
I don't know myself.

I'm not ready for a relationship.

The way I've behaved has caused her huge distress.

She doesn't know if anyone in the world can provide the level of safety she needs.

We also started arguing over details of past conversations. Things like whether I talked to Rachel for 30 minutes or an hour the last time I saw her. My girlfriend believes I've changed details multiple times and views that as dishonesty. I genuinely think some of these are normal memory differences and not lies.
Two nights ago we had another conversation. I explained that this wasn't about Rachel being so important to me, it was about principle. My girlfriend responded that this was bullshit, that I had made my choice, and hung up.
We haven't spoken since.
I sent her a long letter explaining my position, acknowledging my mistakes, apologising for the confusion I caused, and explaining why I changed my mind. She had already read the letter before our last call.
What I'm struggling with is figuring out whether:
I'm being stubborn and selfish and should simply cut Rachel off.

My girlfriend's request is understandable but incompatible with my values.

We're stuck in a cycle where she needs a level of certainty and reassurance that I struggle to provide.

This relationship is fundamentally incompatible despite both of us caring about each other.

I genuinely want honest feedback, including criticism.

What are my options?