Withing the first two weeks of getting my permit, my wife accused me of being obsessed because I was breaking in a new holster (x2 now) and always had the weapon near me.
I started talking to her about the fact that you can not pick and choose the moments that you would be attacked and that she should start keeping the house gun with her when I am at work or out of town. She replied with "I refuse to live in my own house and act like a paranoid victim!"
"When someone breaks into the house when you are home alone, then you will be the victim, and don't think that if you are upstairs that you will make it to the basement to get the gun before they get you."
It was about that time that our quaint little town started having daylight break ins on a daily basis...two blocks away.
She may or may not think that I am still obsessed, I do not know, for she makes no comment about it. I call it situation resolved.
To the OP, I do not know you, or your girlfriend, so my giving any advice would be inconsiderate at best, so please do not take the following very seriously.
Personally if it were me, "This is who I am, I don't try to change you, please do not try to change me." And for entertainment purposes, if she gets cranky about it, "Why don't you come down off your cross, build a bridge with the wood, and GET OVER IT!"