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Short Version
Using DXVK prevents the level-loading crash with AMD Vega GPUs, but lowering graphics settings will likely be necessary as performance will be lower.

Long Version
Using DXVK, a project meant to run Direct3D games in Linux (but works in Windows) using Vulkan, prevents the crash that occurs while starting a race in Carmageddon using AMD Vega GPUs.

A word of warning: the way DXVK works could be detected as a cheat by some anti-cheat programs. I don't know if Carmageddon has cheat detection, or bans as a result of it, so this may not even matter.

*Get the latest release of DXVK here:
Version 1.6.1 was tested for this post.

*From the x32 directory within the archive, extract dxgi.dll and d3d11.dll to CarmageddonMaxDamage\bin. This should be the same directory where Carmageddon_Max_Damage.exe is located.

*You should now be able to play by loading the game as you normally would. Unfortunately performance will probably be lower, so you will likely need to lower some of the in-game graphics settings.

Hopefully this helps. This works for me with my Vega GPU. I think there is a similar crash with RX GPUs. If anybody can confirm that this works with RX GPUs, please let me know.