So I think a variant of this approach is useful and a variant of this approach is really harmful. If you say "fuck it, she's not important," you'll be conditioning yourself not to care about her or even actively resent her for "making" you anxious. That way lies a lot of badness.
Nevertheless, I do think it's handy to come to terms with the idea that if she decides to break up with you, then it's not the worst thing in the world. It's an admittedly sucky but manageable state of affairs. You will be a finite amount sadder than you were when you were single! And although you have some influence on her decisions, you have no control over them. So think "I have done everything in my control in this situation. Now I will go play video games/exercise/whatever." This is a more detailed, more accurate, healthier variant of "fuck it, she's just a girl."
Fantastic girls are important! But they're not your whole life! But they are also not unimportant! There's a large range in between those two!
I agree with a nitpick: you may condition yourself to not care about her. You may also condition yourself to not care about whether or not she responds even if you do still care about her. More accurately, you're conditioning yourself to care less about these things, which may or may not result in not caring at all. And to be fair, part of the problem is that you (the hypothetical you) care too much about whether or not she responds/want to break up with you/whatever and maybe you care too much about her specifically.
I basically want to push back on the id...
I started going out with a fantastic girl a couple of weeks ago. Everything is great, except that whenever I've sent her a text message or email requesting something and haven't received a response yet, I experience significant dysphoric anxiety, fearing that her response will be not just "no" but "no and I don't want to date you any more". This is due to brain chemistry or personal history, take your pick—either seems like a possible explanation to me. But there's certainly no evidence supporting the idea that this is likely to happen, nor is the anxiety helping me prevent it or helping me in any other way.
Does anyone have evidence-based advice, or pointers to same, on dealing with this kind of issue? It is the only splotch on what have otherwise been the best two weeks of my life.