This is called order-independent transparency and is basically impossible (or too performance intensive to be useful). This is because transparent objects do not write to the depth buffer, so there is not an easy way to make then draw on top of each other with proper depth. In general, transparent objects draw in back to front, which normally works fine, provided your scene doesn't have a lot of overlapping transparent surfaces. There are a few things you can do. Adjust the draw draw mode for certain objects, or force a drawing order.
If you only have that one object in the middle, then setting the parameter on the material to draw mode always might work. But in a more complex scene, this can cause issues. It will also hide the particles that are behind it (if they have depth testing on) but it may look less like a glitch. Changing the draw order will only work in scenes with a fixed camera and predictable overlay. In your case, the particles are both in front and behind so it may not work. This is called Render Priority, but I'm not sure it will help here.
