Is there that big of a security risk if they can read the contents of your clipboard? The only example I can think of is if the app is a webview that you use to login to sensitive accounts and it scans the page for a login/password field and saves the login and sends back the clipboard info if found. It seems like reading random clipboard info isn't going to get linked to anything though (please correct me if I'm wrong).
I'd say that's a security risk and it's severity depends on the data you have on your device. The example you state is pretty serious: being able to get the master password from your Android Keypass file or LastPass master password would be a game-over situation!