I'd like to use the Ionic UI framework with Reactive Coffee and without Angular. Is there anything stopping me?
It looks like there's not really any need for Angular in Ionic, but I keep reading vague suggestions that Ionic is intimately bound up with Angular. Is there any sense to this?
Ionic (currently) depends on AngularJS. See http://ionicframework.com/docs/overview/
"Ionic currently requires AngularJS in order to work at its full potential. While you can still use the CSS portion of the framework, you'll miss out on powerful UI interactions, gestures, animations, and other things. In the future we'd like to expand beyond Angular to support other frameworks."
I expect if you want to try and remove Angular, you will either get an unpredictable framework or something very feature-less (e.g. routing, 2-way data binding, etc)
It depends on what you are saying as a UI framework. You can definitely use the CSS markup as you want. However, there will be a lot you can't do because of the JavaScript that handles a lot of stuff or even directives they've built. I've built some sample apps with ionic UI alone, but I also didn't use anything like the Slidebox, the side menu, ionic gestures, and a lot of other stuff they have. You'll have to keep that in mind and build around it. It is probably like using jQuery mobile for UI only and not using any of the paging and attribute markup.
However, after building an application with full use of ionic/angular, I don't want to stop. That is just a personal opinion.