Downloaded Popular Photography + but when I tried to purchase the yearly subscription, I get "in-app purchases not allowed". I'm guessing there is store or iTunes setting I need to change, but I can't find one.

As long as you're signed in to your Apple account, there's really nothing else you need to do on your end to make an in-app purchase.

This is what their FAQ says on their website:

Pushing up with two fingers at the bottom of the screen reveals an Issues button. Tap this to open your library of issues and to access the in-app store, where you can subscribe to the magazine and buy single issues. Tap the price, confirm your purchase, and the issue will appear in your library. There you can tap the arrow to download it.

If it's not working I'd contact them (there's a support link on the iTunes app page for the product). If they don't respond or you still can't get it sorted out I'd report it to Apple. Open iTunes and access your account. Under purchases you can click on the item and then click on the "Report A Problem" button. Apple is very good about getting back to customers and will often refund the price of a problematic app. I don't think you paid anything initially, but they should still be made aware of the problem.

FWIW there seems to be a high number of complaints about the app, so it looks like the developers haven't quite gotten it right.

Hope that helps and let us know how it goes!