Could you please share a bit more about your scenario?
Do you create a canvas app based on your SP list, and save the form data back to your SP list?
Do you mean that the end users of your app don't have enough permission to access your SP list data source?
Could not the end users run your app even though you assign proper permission to them?
When you share your app (connects to your SP list) with other users (who are in your Organization), if they want to run this shared app, they must provide their own credentials to access the SP list data source. If they don't have proper permission to access your SP list data source, they could not run this shared app.
More details about sharing an app within PowerApps, please check the following article: