It's free and open software we specifically give the right to modify and redistribute.

But not the right to distribute with an intact trademark. No open source license provides that right.

If the Blender Foundation one day decided that only the Windows and Mac App Stores can distribute Blender, yes, Linux distributions would be forced to use a different name.

Is there legal precedent for that claim?

Absolutely.

1. Just read the license. Never is a trademark granted. Source code can and is granted completely independently of trademarks (otherwise, as one example, how does Apple license iOS SDKs without permission to use the name “Apple”? It’s just a more stringent license than a FOSS one.)

2. It’s already happened, Debian wanted to change Firefox, Mozilla said no, lo and behold we had “Iceweasel” for a decade.

https://en.m.wikipedia.org/wiki/Debian%E2%80%93Mozilla_trade...

3. Trademarks never expire, unlike patents, trade secrets, etc. Unlike source code, the trademark owner has near-absolute leeway in how they are used.

I think you're misunderstanding trademarks. As an example: if I buy a 12 pack of Coke, I can set up a table and sell them one can at a time. Trademarks require that I don't present that I'm sponsored by Coke, or label my non-Coke as Coke, or a variety of other things that would confuse consumers. That's the entire premise of trademarks: avoiding consumer confusion.

To your example: Debian had to rename their package because they were making modifications to the code of Firefox, so it wasn't Firefox anymore.

OBS could try to make the claim that how Fedora is packaging their code modifies the code, but that's way more tenuous given that building the product with different versions of its dependencies isn't really changing the code.

Considering that trademarks have a long case law with being used to force redistributors offline (i.e. to force my app to not be available on Download.com); I think it is fair to say that it is well established that a trademark gives the owner total distribution control except where the first-sale doctrine intervenes (resale of a product acquired through a legal seller). That doctrine only exists for physical products though, and specifically for items that can be “bought.”

Can you cite one of those cases?

In the real world, Coca-Cola would "force a redistributor offline" by not selling them products, and setting up agreements with their distributors to limit who they can sell to. That's not trademark, and it doesn't transfer to free software.

I think it's easy enough, ignoring the technical details of why, to just look at the results: the version of the app in fedora's repos is inferior to that on flathub produced by the developers. Exactly why this is the case is irrelevant, what matters is that users are getting confused, thinking they are getting an official version of the product, and that this is causing damage to the developers who own the trademark (extra effort in dealing with bug reports, loss of reputation).

Firefox on Debian was called IceWeasel because they wanted the right to change to code if needed.

Sure. But having the legal right to do something doesn't mean that you should do it, only that you are allowed to do it.