Original letter from A Practical Wedding.
A panic disorder is not something to push through to make your family and wedding guests happy. Making everyone else happy with the price of you vomiting from anxiety on the morning of your wedding is not a price that any reasonable person who loves you should expect you to go through with, no matter how respectful of tradition anyone wants to be. Nor is it rude to invite folks only to the reception rather than just the ceremony.
However, similar to the response in this letter about eloping and family's reaction to that, you won't be able to control other people's reactions to your decisions. I hope people will be understanding and compassionate, but probably at least some people will not be very considerate or kind. I'm sorry about that. Tradition is legitimate value to have, but when put up to your health, you get to choose your health.
When it comes down to it, when others end up saying, "why can't you 'just' have a church ceremony like everyone else," they are kind of saying, "why can't you just not have an anxiety disorder"...which in a way, is something that you probably have common ground with them on! But wishing the disorder away is not a strategy that's going to succeed. You can be respectful to family that is being pushy about your decision to break from their vision for your wedding, while still having confidence that your choice is the best way to prevent your panic disorder from ruining your wedding: "Yes, I always thought I'd get married in a church as well, traditional weddings are very beautiful. It's not going to work for me. I hope you'll be able to celebrate my marriage with me even if my wedding isn't quite what you're used to."