If you have set up domain mapping for a multisite, you may come across this issue when you try to log in to a mapped domain, with message: ERROR: Cookies are blocked or not supported by your browser. You must enable cookies to use WordPress.

There are 2 most common sources of this error.

#1: Caching plugin

If you have a caching plugin, go ahead and clear all cache. Then, clear your browser cache and do a hard refresh on your browser. This in some cases will fix this problem.

#2: Add code to wp-config.php

Access your WordPress installation files via FTP or your host Control panel and find the PHP file labeled wp-config.php in the root on the directory. Add this code below:

 define('COOKIE_DOMAIN', $_SERVER['HTTP_HOST']);

Refresh your browser and try again. It should fix the problem. You can learn more about this issue on WordPress documentation here.