Chirality-neutral string
You don't say what you are trying to make or do so I can't help there, but what follows addresses your question about twist in string.

String is technically a yarn.  

The two major classes of yarn are Spun and Filament.

Spun Yarns are composed of individual fibers that are "spun" (by various means, manual and mechanical) together into a longitudinal structures called a yarn.  What holds the fibers together? Why doesnt the yarn just fall apart into loose fiber? The physics that hold the loose fibers together is supplied by twist.  Low-twist yarns are looser and less stable than tighter yarns - think of a loose fluffy (low-twist) yarn in a soft sweater vs. a tight (high-twist) yarn that is woven into a smooth dress shirt fabric.  Even sewing thread is technically a yarn and has twist for strength and stability.

Filament Yarns are zero-twist yarn structures.  Filament yarn is extruded (again, via various methods) and is not composed of fiber held together with twist.  Examples are synthetic monofilament like fishing line, and the monofilament that is used to weave some outdoor fabrics and furniture, and some types of indoor-outdoor carpeting. 

The twisted string structure you show in your question looks to be two yarns simply twisted together.  The twist in the red and black yarns holds each of them together individually, but simply twisting the two yarns together does not produce the physical cohesion between the two structures that mimics the twist imposed in a fiber spinning process. That's why ropes and braids will easily unravel.

This is a simple explanation, it's possible to get a material science PhD in the physics of textile spinning, so there is much more info out there.

Hope this helps.