Of course, there are ways to solve the "Liberal Paradox". One way, is to respect each others seemingly contrary philosophies. By respecting people's freedom to install both free and non-free software, both can flourish.
Free software and proprietary software can and do exist at the same time.
My problem is that some free software advocates don't respect my right to run proprietary software.
I don't think that the GPL 4.0 should read "if you run any non-free software on this system, whether you distribute it or not, you are in violation of the GPL. In fact, if you sell any software, you may not use any GPL software."
There must be compromise. It should not be some sort of inchoate offense to supply or conspire to give or sell non-free software to GPL users. It should not be a violation of the GPL to help others install proprietary software.
Interestingly enough, your example illustrates my point: the US Constitution does NOT outlaw all slavery. It preserves indentured servitude for felons.
The US Constitution also protects political speech absolutely, but commercial speech is less protected, allowing false statements by companies to be prosecuted under consumer protection statutes.
Similarly, the GPL should NOT outlaw all proprietary software and hardware. It should preserve freedom, but allow users to freely install the software they want to install, and to use any computer for any purpose.