Of course, it is important to consider that an ‘excessive use of firewall rules that open’ can compromise the functioning of the proxy. For instance, if you open port 80 in the firewall rules, the web filter might become ineffective. (In this case, if you remove the proxy from the client, you would be able to browse, only on port 80). Therefore, it’s advisable to only open what is necessary.
It’s important to strike the right balance between openness and closure.
The possibilities are endless. I’ll mention some examples:
- You can set a firewall rule to ‘exempt from the obligation of using the proxy’ one or more groups of IPs from the green, blue networks.
- It is possible to “free” only the pop3 service port.
- The combination of 1 and 2.
- And much more.
Think carefully about what you want to do. I believe I can help you ‘translate into firewall rules’ your decision. 
I think this can be helpful for you:
Good job 
.