This may help Create or use your Apple ID without a payment method - Apple Support
If you are setting up an Apple ID for the first time it should not require a payment method, if on the other hand you have an existing Apple ID and you access one of the stores for the first time a payment method is necessary, but once that first access is done you can then remove your details by selecting “none” under the relevant section.
If you say all was working fine before I can only assume something has reset the process, I would try entering your details, make a free purchase, delete your details by selecting “none” and then try to download another free App.
If when trying to remove your purchase details the “none” option is not available there is a link to talk you through the process to correct that situation.
Trust the above helps.