Are you allowed to promote a Patreon page on your iOS app? Under section 3.2.2 (iv) of the App Store Review Guidelines, it says that the following is unacceptable:


Unless you are an approved nonprofit or otherwise permitted under Section 3.2.1 (vi) above, collecting funds within the app for charities and fundraisers. Apps that seek to raise money for such causes must be free on the App Store and may only collect funds outside of the app, such as via Safari or SMS.


Based on the above, what would be the implications of displaying a message such as "Support us on Patreon!"?
Let’s assume you’re not a charity or fundraising for one.


Technically, no since in 3.2.1 (vii) it says you’re allowed to promote voluntary giving, provided 100% of the funds go to the recipient — but Patreon takes a cut of the funds pledged / gifted. 
Realistically, probably yes. If your app is otherwise fine, Apple might not reject you solely for having to pay processing fees. 


As long as you’re not just trying to dodge in-app purchase, I would say make your app and submit it for review. Also, look at IAP for a tip jar I addition to the patreon option. People can and will tip you if they love the app. Also, worst case is you have to find a payment processor where you pay all transaction fees up front or separately so Apple can see 100% of the linked gift goes to you.

Also, if this is all your app does, don’t bother. You’ll need a compelling app that provides obvious value for free or paid and can’t just be a “here’s my patreon, fund me” shell.