You can try to reject the notion of copyrights and licenses, but that quickly runs into practical problems with the law.
In all countries that have ratified the Berne convention on copyrights (which is nearly all of them), copyright law stipulates that as soon as you write down your thoughts, then that record is protected by copyrights to the highest extent. There is nothing you need to do to get copyright protection and even nothing that can prevent it. The only exception is if you are writing something that is explicitly called out in the law to not be covered by copyright protection1.
As copyright protection is automatic, the only way around it is to grant a license to others to perform actions that are otherwise reserved to the copyright owner, or to disclaim all rights and to dedicate your work explicitly to the public domain (which is not possible in all jurisdictions).
The first option would be contrary to the stated intention of rejecting copyrights and licenses. The second option might work, but I am not sure how well you could build a community/movement around it. It will not prevent the "believers in copyrights" from using your code, because code in the public domain is free to use for all.
: Those exceptions are typically government documents intended to be widely circulated and copied, like law texts