Question 

Which domains do I need to whitelist in order to allow DNN to keep working normally? I would like to block all other domains.  

Solution:

You would need to whitelist the following domains:

https://update.dotnetnuke.com
https://dnnapi.com/
https://www.dnnsoftware.com/

Whitelisting Google would only help if you would need to re-connect your Analytics account to DNN at some point in the future. The way it works is that you should whitelist DNN which leverages your Google account to display the data. The connector makes that work, so you shouldn't need to whitelist Google unless you need to set up the connector again, at which point you will need access to your google account to do so.

Credits: Radu Vaduva