How is this supposed to look on Windows, and have you tried the latest stable driver?
I know a few people tested the game on RADV and nobody complained about rendering issues so far, so I would assume it works fine for them.
I installed a stable driver and made some day/night comparison screenshots under roughly the same conditions.
Fedora 29 (Kernel 4.20)


Windows 7 Pro


Any chance you can record an apitrace? This doesn't look right, but it's impossible for me to debug this since I don't have the game (and to be perfectly honest, this is a game that I'll refuse to get).
Sorry, I was not successful regarding the apitrace. With nvapi64 disabled I can get it to start without complaining about an outdated NVIDIA driver but the title screen does not look right (almost completely in greyscale). After login and during the first loading screen it always crashes with a DirectX error.

Upon looking into the wine output I also noticed apitrace loading & unloading right from the beginning. I used the latest msvc binary from https://people.freedesktop.org/~jrfonseca/apitrace/. So maybe I misread the documentation.
Used call:
WINEPREFIX=<PATH_TO_PREFIX> <PATH_TO_WINE> <PATH_TO_APITRACE_EXE> trace --api dxgi <PATH_TO_ANTHEM_EXE> &> wine.log
WINE log:
000b:fixme:winediag:start_process Wine Staging 4.4 is a testing version containing experimental patches.
000b:fixme:winediag:start_process Please mention your exact version when filing bug reports on winehq.org.
wine: cannot find L"C:\windows\system32\winemenubuilder.exe"
000b:err:wineboot:ProcessRunKeys Error running cmd L"C:\windows\system32\winemenubuilder.exe -a -r" (2)
0024:fixme:file:FindFirstFileExW flags not implemented 0x00000002
0024:fixme:netprofm:connection_point_Advise 0x187e18, 0x99bf4c, 0x99bfb4 - semi-stub
0024:fixme:netprofm:list_manager_GetConnectivity 0x187df8, 0x11dfd78
002f:fixme:winhttp:get_system_proxy_autoconfig_url no support on this platform
002f:fixme:winhttp:WinHttpDetectAutoProxyConfigUrl discovery via DHCP not supported
0030:fixme:toolhelp:CreateToolhelp32Snapshot Unimplemented: heap list snapshot
0030:fixme:toolhelp:Heap32ListFirst : stub
apitrace: loaded into C:\Program Files (x86)\Origin Games\Anthem\Anthem.exe
003d:fixme:ver:GetCurrentPackageId (0x24f470 (nil)): stub
apitrace: unloaded from C:\Program Files (x86)\Origin Games\Anthem\Anthem.exe
warning: Z:\home\user\Software\apitrace\apitrace-msvc\x64\bin..\lib\wrappers\dxgitrace.dll was never used: application probably does not use this API
....
Ah right, games re-launching themselves a dozen times before actually starting up. Fun times.
Please try this: https://github.com/doitsujin/dxvk/wiki/Common-issues#apitrace
No luck getting it to run and do an apitrace (without DXVK) but the dlls in the game folder. Without the dlls and just wine-staging it starts but crashes on the first loading screen with the DX error above.
I have minor graphical issues on RADV as well, birds shimmer in neon colors, if it's raining I see rain and projectiles flieing like I was shot at and some explosions and water or mud Form a bubble when jumping in that pops up and does not look right. Same goes for a kind of eye of mordor effect, which should limit my POV but makes the screen flicker instead in red and green.
Very hard to describe.
I upgraded my cpu now and run at a bit more fps.
I will try to do an apitrace in the next days.
OK, I wasn't able to do a trace as well, it crashed the GPU driver on the first loading screen. After trieing to revert back, game kept crashing, so I deleted it and reinstalled. That really worked wonders, there is a new patch out today and I know have solid 60 fps in the menu and fort Tarsis and the game runs at 45 - 55 fps, so a huge performance increase on the r7 2700x and vega 64.
In the settings menu the patch has ambient occlusion auto disabled, I don't know if that did the trick but it improved massively. From 20 minutes of playing, as far as I can tell, my gfx glitches are gone, so prolly it was game related.
OK, I wasn't able to do a trace as well, it crashed the GPU driver on the first loading screen. After trieing to revert back, game kept crashing, so I deleted it and reinstalled. That really worked wonders, there is a new patch out today and I know have solid 60 fps in the menu and fort Tarsis and the game runs at 45 - 55 fps, so a huge performance increase on the r7 2700x and vega 64.
In the settings menu the patch has ambient occlusion auto disabled, I don't know if that did the trick but it improved massively. From 20 minutes of playing, as far as I can tell, my gfx glitches are gone, so prolly it was game related.
Thank you for testing. For me the rendering issues persist even after updating the game (1.0.4) and the NVIDIA driver (418.56). I did not do a full reinstall but I verified the game files with Origin. On aiptrace attempts the game still crashes on the first loading screen with the mentioned DirectX error.
Login screen without DXVK looks like this:

Not a DXVK issue: I retested it with the same wine & DXVK version previously used.
Either the driver update (430.14), intermediate game patches (1.2.0) or the upgrade to Fedora 30 fixed the rendering issues for me.
In Anthem a lot of not directly lit environment pieces appear almost black. Changing graphical settings or disabling dxgi.nvapiHack has no effect. I wonder if it's DXVK related and worth investigating in your opinion or something else (driver, game bug etc.).
Software information
Anthem 1.0.3
System information
Apitrace / Log files