There’s no way to KNOW what they’re doing, but trust, there are plenty of ways to build trust and plenty of people today that do trust closed source OS’s.
Also, I contend that with closed vs open source there are many of us whom do not have the time and knowledge to know what even the open source OS is doing so primarily we are choosing between trusting a company that could face financial penalties for violating that trust and trusting a community of people and companies to keep each other honest.
This also isn’t a binary issue or a simple one. Some OS’s have huge numbers of contributors, some have single digit numbers… An open source OS with few users and fewer devs may be less trusted by me than Windows/MacOS… I will likely never know which is more secure/private but that isn’t the only aspect of the OS’s and isn’t the only way to build trust.
And even for the people whom could know what an Open Source OS is doing, how many of them will actually check and keep checking as updates come out? Sure that number is greater than 0, but I doubt it’s very high either. Most people I’ve met will check the parts they know we’ll when they have spare time which is inconsistent.
As for the original question of is privacy compromised by “non-private operating systems”? I mean by the design of the question, yes.
The more interesting, to me, question is “is privacy compromised when using open source software on a closed ource operating system?” To which my answer is “maybe”. The OS, as mentioned above, does have access to decrypted information in memory; but there are risks for any business that makes an operating system that intentionally violates the trust that such data is kept private. Financial penalties are one risk, another is a mass Exodus away from their platform.