How do I get this camouflage pattern using procedural textures?

It’s difficult to say exactly what might be the problem without the blend file to look at… But I suspect your parts don’t have the scale applied (Object scale should be set to 1.0 in all axis).

Try to appy the scale to your objects and see if it solves the issue. In 2.80 you can use the Ctrl+A shortcut and choose ‘Scale’, or in the top menu Object >> Apply >> Scale.

https://1drv.ms/u/s!Ap6t_YOv62EQer9fV4zEWR-c4gA

Scale is a bit off ( [1.0, 0.9, 1.0] ) in all objects, but that will just squash the texture a tiny bit. Apart from that, I don’t see any stripes artifacts, at least in my end…

Perhabs you’re using a bugged version of Blender… Have you tried to switch to 2.80RC3? or even update to 2.81 or 2.82?

What does “scale” do?

You have the color ramp set to linear instead of constant.

All objects ‘live’ in their own space (their own coordinate system where the origin is the object’s origin).
This means, all vertices from an object are placed in relation to the object’s origin.

If you have an edge, that looks to have a length of 1 meter in world coordinates but it’s object scale is 2.0, it means that in the object’s space that edge is in fact 0.5 meters … Everything that is using the object’s space will say that 1 meter is in fact 0.5 meters, and all other objects with a 1.0 scale will disagree.

In case of textures using the object’s coordinate space, the same will happen. You might want to draw a circle in a space scaled to [2.0, 0.5, 1.0], but the result will be an ellipse even if for the object, the circle is perfect (because as the viewer, you’re in the world space, and your dimensions are different from the object’s dimensions);

more on this…

So if a texture uses an object’s origin, it may appear stretched or distorted? But if a world scale is applied to it, the textures appear clean and even?

Not quite… If you apply the scale there’ll be no distortion or stretching. And if you use the world coordinates, the texture will be fixed to the world (it wound move with the object).

If you still have glitches with your scene, update your Blender and your Graphic driver.