What does it mean when a hair has transparency issues?

No.
In ts4 the only way to enable CAS transparency is through Simglass shader which is meant for lenses. Lenses do no overlay each other, there is only one plane. Transparency issue happens when one plane is in front of another an both of them have simglass shader assigned. The game is not coded to render the mesh in the right way, it cannot tell which mesh is the closest to the camera and should be rendered first because you are not meant to be using it for hair. So, to deal with it you need to tell the game how to render it.

The reason 3ds max is said to be a better software is because it can replicate the same (it is called sorting) issue within the software while compatible versions of blender cannot. Newer versions can but I do not know how efficient they are (I’ve seen a pic and it looked like a mess).
However, I’ve also seen someone replicate said issue in the compatible version but no one else seem to be able to.

Also, no, there is a modifier that can add the other side of the planes automatically. It’s called solidify and you need to disable Fill rim option




also planes are the worst (most time consuming and troublesome ) way of making hair, I suggest to look for tutorials that are not related to TS4. NURBs, hair system + cloth dynamics, sculpting + retopology are better ways but you need to really look into them