edit: just googled, seems dead these days, but Rocky Linux is more or less the same thing
Before it was Fedora -> Red Hat
Now it is Fedora -> CentOS Stream -> Red Hat
The word "free" is well-defined in this context (I carefully used it in the phrase "free software"). A free software respects the 4 freedoms given in the free software definition [1]. You can run it for all purpose, study it, redistribute it, distribute your modified version.
Within the law, of course. Always. Licenses are restricted by the law.
> RHEL is open source, yet it is also proprietary
That's not possible because proprietary means "not open source" (as defined by the Open source Definition [2]). Or "not free" (as defined by the Free Software Definition).
Moreover, something is open source if and only if it's free software.
(save some anecdotal licenses that are considered open source by the OSI but not free by the FSF, but that's anecdotal and that's not relevant to RHEL).
It's exactly because RHEL is free software, or, said differently, open source, or said differently, not proprietary, that open source / free alternatives like AlmaLinux / Rocky Linux, their friends and formerly CentOS can exist, legally.
Note, open source ≠ source available (which is a necessary condition to open source but not sufficient).
> you have to strip out all references to Red Hat (trademark / copyright infringement)
Sure. That's trademark, and not related to copyright. Open source / free software licenses are related to copyright only. The licenses do offer you all the rights guaranteed by the definition of free software, of course you still have to respect the law by using those rights, including trademark.
Respecting licenses (based on copyright) and respecting brands / trademarks are two orthogonal dimensions of the matter.
You could tell me that see, you can't redistribute RHEL verbatim because of trademark so it's not free software. Wrong. It's right that you can't redistribute RHEL verbatim because of trademark, but that's not enforced by its FLOSS licenses. It's enforced by law (hence my mention of the "within the law" restriction earlier). It's subtle but important nonetheless.
Firefox has similar restrictions. Mozilla allows you to redistribute it under the Mozilla Firefox brand only if you don't patch it too much. Formerly, it was stricter than that, you could not redistribute it under the the Mozilla Firefox brand if you changed anything. GNU/Linux distributions could redistribute it as Firefox even though they patched it because Mozilla explicitly allowed them to do so. That's why Debian redistributed it as Iceweasel at some point, and now as Firefox again. They first decided that they didn't like needing an express authorization, and then Mozilla requirements were relaxed, ways of doing things changed, and using the trademark was fine again [3].
> RHEL is not free
It's not free as in gratis.
It is free as in libre / free software. It's certainly not proprietary. Except for proprietary software it has in its non-free repositories.
[1] https://www.gnu.org/philosophy/free-sw.html.en#fs-definition
Open source software can cost money, and still be open source...it currently exists.
It's not what this word means in this context. Almost nobody uses proprietary this way to describe software, because it's used as opposed to FLOSS, and because it would be useless: a piece of software always belongs to someone unless it reached public domain (which is not many pieces of software). It always has one or several authors, working for someone else or not, so by this definition any software would be proprietary. Why call a piece of software proprietary then if it's always the case?
It's like proprietary protocol meaning "non-standard", "specific". Proprietary has several meanings, depending on the context.
You need to use the words the way they are by everybody to be understood correctly. Or stick to your usage and you'll end up in futile debates again and again. Or try to convince people that your usage is the right one if you have strong reasons to do this. But good luck with that. Proprietary software is used with this meaning since the 80s and it's not controversial AFAIK.
> Open source software can cost money, and still be open source...it currently exists.
I know, I work at a FLOSS company.