Why is beryllium transparent to x-rays?
The amount of X-rays absorbed by an element depends on the size of its atoms (its absorption cross-section, specifically, as affected by the size of core orbitals that contain electrons that can be excited by X-ray absorption, and the number of electrons in those orbitals) and how many atoms are packed into a given volume. Big atoms that are close together can absorb more X-rays than small atoms that are far apart.

Beryllium has very small atoms (it has a very small electronic core, with only two electrons in it), and very low density, so it will absorb relatively few X-rays compared to other materials.

According to this page, 37 % of X-rays with a wavelength of 0.56 nm will be absorbed by beryllium window that is 23.5 mm thick. If the window were made of aluminum, it would only have to be 1.4 mm thick to absorb the same amount of X-rays, and if it were made of lead it would only have to be 13 μm thick.