I think that was also the common approach to paranoia about your privacy pre-Snowden. But he kind of ended that discussion for many, although denial or ignorance is probably better for your soul indeed.
He didn't end the discussion, he presented evidence. When you receive updated evidence you should update your beliefs.
He presented good evidence that big corporations are co-operating with the NSA, or something, but he didn't present any evidence at all that regular Linux distros are monitoring all your keystrokes. As far as I know.
To just wildly speculate about mass surveillance without evidence is just baseless conspiracy theories, you really have nothing to worry about. Hope that helps.
On a related note, not believing some things because you cannot prove them is a road to naivety.
For me personally, based on the plethora of evidence given by other online platforms and applications, I think it's perfectly sane to assume that yes, your data is being slurped and logged. Maybe that's not a bad thing, maybe it is, but at this point I think that ship has sailed.
Can I prove it? No, mostly because the manufacturers have specifically designed it in such a way to be unprovable.
The fact that our currently popular operating systems don't enable users to trivially 'disprove' such possibilities really shows how shitty they all are
Well apart from monitoring network traffic, with Ubuntu you can examine the source code for anything that you don't trust or dive into what system calls an application makes by using "strace".
Well you can try monitoring Windows network connections, but Microsoft do seem to love obfuscating it with connections to multiple different domains that they own.
You can't even look at the Windows source code, so your question about reproducible builds seems to be moving the goalposts somewhat.
Also, is there something like "strace" on Windows?
Edit: just looked it up and Ubuntu doesn't enforce reproducible builds, although with their new "Monthly Snapshots", Canonical is moving towards reproducible build pipelines.
The necessary technical and UI/UX difference would be capability-based (https://en.wikipedia.org/wiki/Capability-based_security) microkernels like Sel4 or Genode combined with high level user interfaces that allow one to monitor and control the rights and actual resource access and usage of programs
However, it is possible to audit the Ubuntu software against the source code which is something that you cannot do with Windows. That is a technical difference even if you don't acknowledge it.
Also, Linux does make it much easier to determine your level of trust as the different components can be analysed/verified independently (although systemd is a bit of a monolith) whereas it's a lot trickier to isolate Windows components.
The standard for holding a belief isn't "can you prove it is not so?", but "on the balance of evidence, is it likely to be so?".
If you believe everything you can't disprove, you'll hold an awful lot of bizarre and contradictory beliefs.
In the past I have spent some time believing some things simply because I couldn't disprove them, it is not good for the soul.