Unless I'm mistaken, he's already done that. He just had to rename it to something else. So AFAICT there is nothing to see here. As you say, F-Droid already does that with several packages (and even renames them when requested).
Some people are clearly angry, but it seems that this is yet another case where people are angry because they don't understand the GPL or don't understand the situation (or both).
If you're talking about https://fdroid.eutopia.cz/, I don't think that's the same thing. This isn't Moxie's and because of the name change, not completely moxie's code unless he's got a build flag for changing the name everywhere, not sure.
I download things from F-Droid, mostly for convenience and security since I get notified about updates, but I understand it is another person/group I need to trust. I trust, for whatever reason, that they will build directly from source and update frequently.
Ways this could go, as I see it:
0. Moxie's code, moxie's build, Google's repo - The current way I know of getting moxie's build, but you have to trust Google as well.
1. Moxie's code, moxie's build, moxie's repo - I think this would be best, and what I was talking about.
2. Moxie's code, fdroid'd build, fdroid's repo - what I would also like, but moxie publicly discourages unofficial builds so fdroid doesn't want to touch it. Up to them.
2b. Moxie's code, moxie's build, fdroid's repo - a hypothetical some people have floated, but fdroid won't host binaries they haven't built from source and I don't blame them and moxie wouldn't provide an official build outside of Gplay either way.
3. Moxie's code modified with new name by 3rd party, 3rd party's build, 3rd party's repo - eutopia.cz's build and repo. Another person to trust to build correctly and update frequently
I don't think it's just some people being angry. I think things could be better, but it doesn't sound like they will. Moxie wants F-Droid to provide services similar to what GPServices provides before he'll do 1. F-Droid will never do this(hopefully). So we have to live with 0 or 3. I think scenario 1 > 3 > 0, other people think otherwise.
Some people are clearly angry, but it seems that this is yet another case where people are angry because they don't understand the GPL or don't understand the situation (or both).