404.php only works if I'm logged in. Everybody else redirects to wp-login.php - why?

Question

I have this "Forum Engine" theme and want it to be private. (No it's not bbPress, that was my first question too.)

So the theme (Forum Engine) has a "page" called "Threads Index" that is static on the homepage. I set the page to "Private" and fine, the site is private and everyone gets a nice 404.php page if they aren't logged in.

Well, three times randomly (last night, earlier today and just now) the homepage just disappears and does not show the 404 page. Instead of showing the 404, it redirects people to wp-login.php

I don't want random people directed to wp-login.php, I want everyone that's not logged in to see 404.php

After more testing, I found that a random URL like http://example.com/testtttting redirects to the 404.php properly (good) for users that are logged in. But users that are not logged in, http://wallstreetalpha.net/testtttting redirects to wp-login.php (bad).

More digging with Firebug. The homepage does a "302 Moved Temporarily" redirect to http://example.net/wp-login.php?redirect_to=http%3A%2F%2Fexample.net%2F&reauth=1

Answer 1

The solution was straightforward, though it took me forever to find it.

The website has a "Members" plugin (by Justin Tadlock) and the option "Redirect all logged-out users to the login page before allowing them to view the site." was checked. So I just unchecked that box, problem solved.