Hmmm . . . for the "Anonymous" role I've checked "Allow" for all the following permissions:
View Page by others
View own Page
View Projection by others
View own Projection
View Contact Page by others
View own Contact Page
View all content
View own content
(I don't see "View Content Item", but I assume that's covered under "View all content".)
But I'm still getting "Access Denied" when I try to open my home page without being logged in.
Anything else to try before I go digging down into the code?