Others have already said what I came here to say, which was to figure out how important socialism is to you and decide whether she's worth it. Well, duh

what else are you supposed to do? So instead I'll give you my opinion on how important economics is to me, and what I decided after a similar bout of self-reflection.
I like economics, I read mostly economics/finance/business focussed newspapers, my job is highly dependent on my knowledge of economics, and I think about economics all the time, but I can't imagine defining myself as the sum of my views on the subject. It's just such a bizarre, trivial thing to take offense to. I mean, I can understand that you believe passionately in socialism, but I can't understand why this should matter in personal relationships. Fundamentally, I just don't believe that your political views should have a bearing on your worth as a human being.
What I personally found in the past was that, when I got into arguments with people over politics or economics, I felt like I had to be considered right. Note the wording: it wasn't enough just to
be right, I also had to be
considered right by other people as well. And I too would think about the argument all too much, and come up with rebuttals and refutations even the next morning on the way to uni/work and so on. The reason for me doing this was two fold.
First, I didn't feel confident enough in my own political and economic views, and so I was really trying to prove to myself that I was, in fact, correct. And partly in order to do that, I sought the other person's approval and validation. Now, I'm a much more confident person, and frankly, I
know when I'm absolutely, 100% correct, and when I'm merely giving my opinion on a subjective, unknowable, and usually marginal issue.
Second, I identified
too much with "being a political and economic thinker". That is, the political and economic views that I held had become part of who I was as a person. They defined me as a person and became part of my identity, and therefore, when people disagreed with my political or economic views, I felt like they were attacking
me. Now, you may feel that having such strongly held political and economic views is a good thing, but I don't think it is. I think it's intellectually limiting in and of itself, but also, externally, it causes the kind of interpersonal problems that I was having at the time. Having such strong views made me a less happy person.
Anyway, I don't know whether, on self-reflection, you will find that you feel the same way when arguing with people about politics and economics. But if you do, I highly recommend detatching your identity from your political and economic views. In doing so, you may find that
her political views don't detract from her worth as an individual, friend, and girlfriend.