What is the ruling on money earned from a website that displays cartoon series taken from sources that may not respect intellectual property rights, knowing that the site is also directed at non-Muslims? And would I be sinful if I left the site while my partner continued to operate it?

Such animated films are not free of caveats. If what is published on the site contains any of these caveats, then it is not permissible to publish it, and it is forbidden to take money for it, even if most of the site's visitors are non-Muslims. However, if what is published is permissible in itself, then its ruling depends on the permission or prohibition of its producers, because intellectual and literary rights are protected, and the default for these films is that their rights are reserved, so it is not permissible to publish them except with the permission of their owners. Repentance is obligatory for publishing forbidden films, and repentance is by deleting all forbidden films and not publishing them. If the partner does not respond to removing them, despite the other partner's effort to do so, then the partnership with him must be dissolved.