Since you mention that the behavior is seen in other clients the cause seems to be somewhere in the connection between the parties.
Some practical info to add to your post and some tips on how to request support:
However since the behavior is also seen on Android (I presume you use them form the same network?) this leads me to conclude the issue you are experiencing is not caused by specific software on your devices and this forum would be the wrong place to request support for your issue.
For reference I use Evolution & Android have 2 gmail accounts and do not experience the issues you describe.
You should contact your ISP if you got the modem from them to replace it with one who does have settings like that.
Another way might be using an UPnP client to punch a hole you need if your modem reacts to UPnP.
If all fails just disable the firewall on the modem completely and use the firewall of your Linux
Your ISP/ might block access to external sites for a variety of reasons. The traffic you generate is a flag in a filter that is targeted to block on the ISP box:
Malicious activity (this could be the previous user of the IP your traffic originates from of you share your connection with something/one malicious)
Protocols that are valid but are know to be misused/exploited/generate to much effort for the ISP (older or legacy/expensive traffic)
Your ISP blocks services that they sell/provide themselves, I doubt this but it can happen.
The ’ high’ filter is suboptimal.
1 Check that the connection is made in a ‘modern way’ eg do not use imap or pop3
2 Contact your ISP (or your ISP user community) explain your issue and ask for a solution.
Some incoherent thoughts:
The high setting might as well be a deny all when something as basic as a secure connection to a worldwide serviceprovider does not function(this does depend on where one lives tho). I am hesitant to give advice on how one should configure ones network since there are different solutions out there and there is no info on the type/provider/country of the connection. As a rule of thumb, most if not all ISP boxes block everything from outside going in and provide NAT & UPnP out of the box (in my part of the world). For more complex protocols (using gmail should not fall into that category) a UPnP solution could be configured.
I am intrigued what high should accomplish on the device since the only option a service provider should provide to keep you safe is the blocking of external traffic and accept internal traffic.
So what are the medium low and none options for?
The high/medium/low/none setting, to me, seems useless and provides a false sens of ‘am I safe’, eg how can one be ’ medium secure’, a internet connection is not a hamburger, but I digress, please forgive me, it is a excellent query on the support page of the service provider, my guess is it is next to the page that gives the advice to not open links you do not trust.