Would uninstalling Play Store and Play Services delete user data on phone? If I uninstall Google Play Store and Play Services will that delete files such as texts, pictures and more. My issue at hand is this error continuously appearing on my phone: "Google Play Services has stopped".
No, it would not delete your files. 

You should always keep a backup of your data anyway. The error you are seeing is because these services are defined as system services and there could be some of the other background services which are are trying to access it.