How to create an Apple ID without putting a payment method in

Read this support article for the various ways to create an Apple account. Some specifically mention entering a payment method. Others do not but it could be part of the "follow online instructions" section. It used to be possible to create an account with no payment method and Apple specifically said that. However, it does not any longer so if you are encountering a requirement to enter one then you are either using a method requiting it or Apple has made it an across-board requirement.

This document explains how to create a new Apple ID (create an Apple Account) --> How to create a new Apple ID - Apple Support