After posting this, I ran a quick test. It appears that when the viewport is set to Preview rendering mode, the crash does not occur. It only seems to happen when I execute a final render.

Further info: the fur in the example file I gave was not actually using the material with the texture. Setting the correct material to the hair system still reproduces the issue, and further testing reveals that simply having a textured material present in the object's materials will reproduce the issue, whether or not that material is used.

I think that a cause is not the matter that you pointed out.
blender crashes for EXCEPTION_ACCESS_VIOLATION when I use the file which you attached.
However, it does not crash when I change some items.
A change point.
I set a order of Subdivision Surface Modifier last.
Probably I think that it is caused by Subdivision Surface Modifier.

Well, that's extra strange, then.

And yeah, EXCEPTION_ACCESS_VIOLATION is the error that gets reported on Windows systems. On Linux systems, the error reported is segmentation fault.

For some reason, I had the subsurf modifier disabled for preview render. After turning it on, the crash now begins to occur when the viewport is set to Rendered mode.

In any case, I did some further testing and found yet another condition for triggering this crash! This condition once again deals with the textured material, and the condition is that the texture is using UV inputs as the texture coordinates. If you instead plug in things like generated or normal Texture Coordinates, the crash does not occur.

This leads me to believe that UV mapping is the underlying problem since the subdivision modifier can change an object's UV mapping. However, toggling the the "Subdivide UVs" option under the subsurf modifier doesn't stop the issue from happening. So, not sure if that's the cause either.

This issue seems to still be occuring as of build 19cc75d