Adding these to your allow list should enable licensing and authentication of Redgate tools to run smoothly. We recommend that you use the DNS names instead of the IPs as we don't guarantee to keep them constant.
DNS licensing.red-gate.com, productlogin.red-gate.com and update.red-gate.com
IP - N/A this changes constantly
Using HTTPS (port 443) and HTTP (port 80)
The full list of endpoints relating to licensing:
The locally (to you) hosted endpoints for the Redgate Client service are ports 22221 - 22223 by default (e.g. 127.0.0.1:22221)