[edit] Glasswire! https://www.glasswire.com/ It's super slick. Apparently the paid version has an "ask to connect" feature.
Personally, I’d recommend using a combination of GlassWire for monitoring system changes and NetLimiter for the firewall.
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¹ — http://www.netlimiter.com/products/nl4
² — http://www.netlimiter.com/Files/ImageGalleries/netlimiter-4-...
Isn't this what e.g. Zonealarm has been doing for 15 years on Windows?
But I can see how this can be a disruptive process, when all you want is some work done. I wish we lived in a place where I did not have to use tools like this.
And, as soon as it's touched, the project maintainers can shut down the SourceForge repos and move on to someplace else.
It's not a guarantee of security, privacy or anonymity, but open source is still your best chance to get any (or all) of the three.
I didn't like the fact that that it is opt-out and not opt-in, but yeah, way way better than Windows 10 for now.
Also note that Canonical took steps to ensure amazon doesn't get to imprint your system by proxying the requests through their server.
Things getting in can damage your data, but that is what back-ups are for. On the other hand, things getting out can leak your data, which is likely to be a one-way trip and, depending on the type of data, potentially a very expensive one.
Of course things getting in can also interfere with your device's normal operation, and in the brave new world of always-online systems and reprogrammable everything, if your system does get compromised today it may be extremely difficult to reliably clean it. The days of booting from a operating system's install CD and reformatting as a reliable recovery mechanism have long passed. This is not a good thing.