As a follow-on to these questions:
What unique fingerprinting information can an iOS7 app collect?
What unique device fingerprinting information can an iOS8 app collect?
Apple has apparently removed the ability to see other running processes in iOS 9, and throttled (and otherwise limited) the ability to test URL schemes. See: https://developer.apple.com/videos/wwdc/2015/?id=703
What remaining device fingerprinting privacy / security vulnerabilities still exist as of iOS 9, particularly those that have no user controls to block them?
e.g., There is still no official confirmation that "integrated" apps (like Facebook or Twitter) are subject to the above limitations. Both Facebook and Twitter claim that their apps are able to access an app list to use to target ads. Twitter's privacy policy hasn't been updated to state that app graph is unavailable in iOS 9. Also note that this capability is often discussed as "installed and not simply running apps"; see link in this comment for example: What unique device fingerprinting information can an iOS8 app collect?
e.g., There have been apps in the app store that show system information like uptime, battery level, disk size and usage, memory size and usage. These could easily be used as elements of a fingerprinting algorithm in a malicious app or in 3rd-party code in an app.
e.g, as always there is basic system info available similar to what any web page can access: IP address, HTTP headers, etc.