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