You and I must be even more dissimiliar than it seems, because my first question here is how exactly is there anything wrong with this? She's out of high school and wants to move out on her own. Dude, this is what's supposed to happen. She's an adult now, it's time for her to go out into the world and make her own way. The whole point of parenting is to make her ready for this moment. Congratulations, you seem to have done it!
You talk about her leaving in terms such as "running away" but nothing you told me in this letter gives any indication that that's how she sees it. She may very well see it like that, but a lot of this dread you seem to feel sounds an awfully lot like you projecting more "I hate my parents!" feelings on your daughter than she may really be feeling.
If she really is like me, then she realizes (just as you do) that your differences are natural. Hell, I hated my parents too when I was young and living under their roof. There were times that I thought I could just fucking kill my dad. The older I get, I realize I'm more like him than I'd ever care to admit. I'm also very different, though, and living under his roof and his rules was stressful and difficult for me. I was happy to get away from home, just as I'm sure your daughter is happy to be doing the same.
But why are you taking that so personally? Were YOU not excited to be "out on your own" for the first time when you left your parents' home? Even if you agreed with your parents and never fought with them, it's still awesome to leave them!
If you want to understand what she's thinking, here it is. She's thinking that she can finally live her own life on her own terms without having to abide by your "compromises" (which are fucking shitty, by the way). She also sees her chance to "prove you wrong" because you think that her way sucks. She wants to get the fuck out there and make a GOOD and HAPPY life for herself.
And one day, my dear ConservaDad, she'll enjoy coming to visit your home. I can't tell you how much I hated living with my parents sometimes and now, whenever I visit, I hate to leave. I've never loved my parents (or siblings) more than when I no longer have to be trapped under one roof with them.
Your shitty attempts at "compromise" tell me that you don't really do well when your children step outside of your control. Oh yes, you let your agnostic daughter stop doing things she was voluntarily doing anyway, but you still made her go to church. No "getting off easy" for her, right? She may be headed the heathen path, but you weren't going to "make it easy for her" were you? That's less about compromise and much about control. But you're like many parents in that regard and I understand it. Now, it's your turn to understand something. You don't have any control over THIS. She's an adult, she's leaving, she's doing it without your help and therefore without any terms and conditions you may have set for her otherwise.
The only thing you have any business saying to her is that you love her and if she needs you, you'll be there, no strings attached. Help her pack, help her move, then leave her alone until she asks for your help. And she probably WILL ask for your help, but not if she feels like you're sitting by the phone waiting for her to call for help so that you can be all like "ah-HA! I knew you couldn't make it without us!" Stow that shit, fool!
Your job, as a parent, was to raise someone who will contribute to society. I think you've done that, even if her contribution is not going to be what you might've wished. Now your job is to let her go and make her own life that only involves you when she's ready.
It'll be hard for you, but it's honestly as easy as just keeping your big mouth shut. Try it, you'll be amazed.
With Deepest Scorn,