I was wondering if this case is allowed for Appstore and Playstore by the guidelines:
User gets in-app message, "Would you recommend this app to your friends?" Button "yes" = appstore rating, button "no" = feedback form and button "close".
If positive, the user basically writes a review, if negative, the feedback keeps the potential negative review away. Is this allowed?
No.
That would be a way to fool the rating system by forbidding negative comments. That's not allowed (and could even put your account at risk).
Well, I can't see any fooling of the rating system. The user can leave a review whenever he wants. Asking for a review when he's in a good mood is simple marketing. Even Apple gives tips and tricks how to get good reviews from within an app.
You can ask users to rate and review your app at appropriate times throughout the user experience. Make the request when users are most likely to feel satisfaction with your app, such as when they’ve completed an action, level, or task. Make sure not to interrupt their activity. The SKStoreReviewController API lets you give users an easy way to provide feedback about your app. You can prompt for ratings up to three times in a 365-day period. Users will submit a rating through the standardized prompt, and can write and submit a review without leaving the app. Ensure that your support contact information is easy to find in your app and on your App Store product page. This gives users a direct way to reach you if they encounter difficulties, and gives you an opportunity to resolve negative experiences that may otherwise lead to poor reviews.
From: https://developer.apple.com/app-store/ratings-and-reviews/
Greetings Brigitte