Firefox on iOS doesn't even exist really, it's a lie. It's a Firefox front-end to Safari designed just to look a certain way and sync settings and bookmarks. Apple won't allow anything more, it's not Mozilla's fault.
Apple allows limited code execution. You can build cordova application and download new JavaScript code as an update. That's fine from Apple's PoV. They don't allow arbitrary machine code execution, like someone getting into AppStore and then downloading and executing malicious code calling private API. But if your code is run with JavaScript engine, it's fine.
Now I don't know about possibility of implementing browser plugins. I guess that it should be possible, but API would be different from other platforms.
iOS has built in content blocking that works with Safari and the newest embedded web view - meaning that you get the same ad blocking in apps like Feedly.
There are multiple ways to embed a webview in an app. The SFSafariViewController is an out of process webview that you can embed in your app. It can share cookies with Safari and it will use whatever content blocker you have installed. The hosting app doesn't have any access to the cookies or any information you type in. Feedly uses this web view.
https://stackoverflow.com/questions/32681511/deactive-ios-9-...
Firefox doesn't use SFSafariViewController. It uses the WKWebView (?). The WKWebView gives the hosting app a lot more control over the webview and whatever you do in the webview is accessible to the hosting app. Cookies, bookmarks, etc. are not available to the hosting app.