Your file hair use "normal map node". If the normal map node> " UV name" is not blender 2.8 default, even though it is correct UVname of mesh, Eevee render cause crush
when you select material slot. To correct it, you need to delete UVname from "Normal map node" . from current scene material slots.

NO! sorry it worked about my scene files,, but downloaded file still cause crush when select material.

With recent build version: 2.80 (sub 35), branch: blender2.8, commit date: 2018-12-08 17:06, hash: e79bb957fc3, type:
build date: 2018/12/09, 17:21

You need to set "screen space reflection> refraction" and, material refraction setting too to render refraction or tarnsparent for Eevee
most of case alpha blend is OK. Though I do not know each property detail, and hope when we set render as eevee
those property auto-set to get more reasonable effect.

I could confirm this issue. my operating system,and graphic card is same as you. I test with newest build (compile)

I found most of scene, which cause these 2.8 crush have material which include normal map nodes with UV set name.
or when I select the mesh (which include normal map node slots) , and select material property ,blender suddenly crush.
To correct it, I remove UV name from normal map node. or set name as Blender 2.8 default "UVmap" . It is not matter, if I use different UV set name for mesh.
I must need to delete UVname or use "UVmap" for normal map editor , UVname.

And if I render armature animation with cube which change scale, only cube animate in out put image. but figure keep same pose (frame 1 to 60)
at this time, I output as mkv format.

I got same problem (windows 10 with GTX980ti, used today build)

Though this report is already confrimed, with my PC and todays build windows 10 64 bit blender 2.8, even though I spilit window and set as UV image editor
I can not move UV edge vertices . Then it is not matter which workspace I choosed. (I set "Layout workspace" and it is default for me)

I could confirm , when I connect normal map texture for the normal map node (with set Eevee as render engine), today build blender 2.8 suddenly crush.
And my sysytem is windows 10 with Geforce 970 Ti

Unfortunately offering files seems almost impossible. It happened about rig realistic humantype figure with hair, with a few cloth only scene. the mesh is what I got from daz. (include some product morph, and use product textures) all material mainly use principled bsdf with glass, transparent sahder. (I remove all my custom shaders) About 2.8 and Eevee (or dev-mode)

Hi I need to re-consider this report.(and hope it confirmed) Because I understand, "Make links >material" can use to see same material (from source). and about some case it work what I expect, but there is clear difference, Between "Copy Material to Others" and "Make links (materilal)

Thanks advices. I could understand, Link material have many advantage, and plan to use it more.
but I may need to test it, to confrim it can be substitute of my current plan.

Thanks to check this report. andyour blend file actually worked, but it was different how set-up material, in outliner.
your attached blend file, "mat_blue" link material for "object" but at same time "mat blue" still keep link with "data" of cube1