Where we part company is here:

The alternative—don’t have any blasphemy laws and let religious people’s feelings be hurt, just as the feelings of the secular are regularly offended by religion—doesn’t occur to the archbishop and people who think like him.

I have no more sympathy for the secular than the religious when it comes to feelings being offended. Nobody’s religion (or secularity, for that matter) offends my feelings. Why should it? Now, if someone’s religion involves replacing my constitutional republic with barbarism, then I’m offended. In that case it’s not my feelings, but my freedom which is threatened.

In the end, Hitch is right: there should be no blasphemy laws. If your beliefs can’t take ridicule, maybe they aren’t worth much.