App Store requiring payment method for a free app.

Just because the app is free to download does not mean it does not have the optional in-app purchases that could use the required payment method. Developers allow you to download the app for free in hopes you will find their app useful and use one of those methods. It does cost them time and money to create the apps and also to provide continual updates. They must also pay every year to provide the app in the App Store. See this Support Article and note step 2 if you cannot download apps in the App Store.

If you can’t download or update apps on your iPhone or iPad - Apple Support

That would indicate your current payment method is not valid and you will need to add one that is. You won't be charged to download any free apps.