... and I think you're rather the cut off your nose to spite your face type who acts on impulse. Stop breaking up with someone before allowing them to explain themselves (particularily if you love them) what you did was totally immature.
It sounds like she's willing to stop all contact and apply a personal relationship boundary along with you which is that neither of you will be texting or hanging with ex's behind the other's back.
Learn to freaking communicate and if aftter communicating you're not going to be getting what you want to be able to be happy, then break up with someone.
Talk to her. You're lucky because she's either too young/naive or she's dumb enough not to tell you to get lost but before you do that, first take the stick outta your ass.
There's nothing wrong with having deal breakers in your relationship but you have to make sure your SO knows what the hell yours are before you punish her for crossing them.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion