GDPR doesn't care about your site, it cares about user data. The big thing with shutting the site down is it might make it impossible for users to request info

GDPR doesn't care about your site, it cares about user data. The big thing with shutting the site down is it might make it impossible for users to request information about their data and/or request to have it deleted. That would violate the GDPR and could land the site in trouble.