Yes I know that Cuba, the DPRK, and China have their own distros, but they're pretty specific to the language and networks of those countries. I use linux because it's free and open source but I use one of those distros that is privately owned and I'm thinking of upgrading to something that is truly communally owned but also has good compatibility with software, especially scientific software. Any good recs please?
Thanks!
I think Debian has the best principles out of any distro. Debian follows a list of principles called Debian Free Software Guidelines (DFSG). You can read the principles and see if you like it.
The thing that I like the most about Debian is that the proprietary packages and FOSS packages are on different repositories. You can install Debian with no proprietary software and leave the proprietary repository disabled to have a completely FOSS system.
https://wiki.debian.org/DebianFreeSoftwareGuidelines
https://www.debian.org/social_contract
The Free / Non-Free demarcation is fairly well explored territory (and Debian is pretty solid on this front, despite falling short of FSF approval). Another thing that's worth consideration and doesn't get as much discussion is the organizational structure of a distribution.
Organizationally, there are roughly two types of Linux distributions. There are distributions which are created as a product or by-product of some company, who's goal is ultimately to make money (through support contracts or hardware sales typically). These are your Ubuntus, Red Hats, Fedoras, Pop_OSs, SteamOSes, etc. Then there are distributions which are maintained directly by a public collective who's sole purpose and raison d'être is the maintenance of the distribution. These are your Debians, Gentoos, ArchLinuxes, Guixs, etc.
As far as these collective organizations go, they vary a great deal in robustness. You could call a Github repository with a pair of maintainers and a dozen or so people reading the issue tracker an "organization."
On the other end of this spectrum, there are distributions like Debian and Gentoo which have incredibly robust organizations with constitutions, bylaws, committees, elections, referenda, etc. Then there are a lot of distros developed on an ad-hoc basis somewhere in-between these two examples.
Having a charter and elections doesn't automatically make an institution good by any means, but governance structures like these have a big impact on the direction these distributions take, and what they are willing to compromise on. The ones which are organized publicly by members of the community rather than by the whims of some software company have done a good job keeping to their principles, and these distributions are among those of the greatest longevity.