IOS – Are purchasing items through apps against the rules of the App Store

Only if there are already tons of apps that will let you navigate, say, The Smithsonian Museum of Natural History." Then that one app for the smithsonian MAY be rejected.

But, I suspect there are not, so you should be fine.

Similarly, since you'll presumably be adding additional apps with different functionality, say the next one is for the Guggenheim, you should be fine. The 2 apps couldn't possibly be used as a replacement for each other.

Apple's concern here is keeping out over-served functionality. There are so many "fart" apps that yet-another-one can't possibly help any user anywhere beyond what's already available. Museum apps are well outside of that scope, assuming you create a quality app with a great UI for museums that don't already have several hundred apps.

Besides a simple "It's Apple's App Store and they'll do as they want to"...

Netflix does not provide any registration mechanism within the app. When you download the app, the first thing you get is a login screen (and a Forgot Password link). Nothing else is present.

Spotify has a registration mechanism in the app, but it also allows you to purchase subscriptions within the app. Rdio uses the same method. (As an aside, Rdio charges more for the in-app subscription than it does if you use their website to subscribe, to account for the 30% cut that Apple takes. This is allowed.)

Basically the answer is, you can provide a registration mechanism in the app, but you must also set up IAP for your paid subscription. Otherwise, you can provide a login screen for your customers who have subscribed outside of the app, but no links to your registration or subscription websites.

Look at the Review Guidelines section 11.14 (emphasis mine):

Apps can read or play approved content (specifically magazines, newspapers, books, audio, music, video and cloud storage) that is subscribed to or purchased outside of the App, as long as there is no button or external link in the App to purchase the approved content. Apple will only receive a portion of revenues for content purchased inside the App