The developer of Museum Shuffle cares about your privacy. Museum Shuffle does not use analytics tools, advertising, or third party SDKs. The app does not store personal information such as name, email, etc. The list of artwork you have saved as favorites does not leave the device. Individual artwork you haved saved as a favorite does not leave the device unless you choose to share it via email, iMessage, etc.
Museum Shuffle does store artwork counts received from the museum to enhance future shuffles. This is done because the museum will only return a maximum of 100 pieces of artwork. If a user has never done a shuffle for bowls, for example, then the app must ask for bowls 1 through 100 (because there might be less than 100 total bowls). However, if a previous search revealed that there are 400 bowls that can be returned by the museum then those additional bowls can be used in the shuffle results. This greatly increases the variety of artwork returned in a shuffle. You can erase these counts at any time via "Erase shuffle statistics" in the settings menu. You can opt-out of collecting these counts using the "Block shuffle statistics" option in the settings menu. These counts are stored locally and are not uploaded anywhere.