These are air springs not shocks (which your car has as well). I would conclude that they indeed put the incorrect part in one of the boxes. The picker at Arnott couldn't have known this.

I can appreciate that it's today for your project but I'd wait till Monday. You have photos and this will help them (as well as the text write-up you posted). Replacing only one side (say the right) isn't dangerous but you'll need to repeat the same procedure (jack up car, remove fuse, undo plastic cover in trunk, undo air lines, etc.) twice.

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2002 Euro X5 (E53) 3.0 diesel (M57)
5 speed manual with UUC short shifter.
Pre-xDrive NV125 transfer case (chain & gears).
Factory Xenon headlights, Spyder LED tail lights
Updated vortex crankcase breather.
Motorsport dead pedal, factory fire extinguisher, factory first aid kit, factory F&R mud flaps, factory PDC

Bilstein B6 shocks F&R
Redline oil has replaced "lifetime" fluids (F&R diff, manual transmission, transfer case and P/S).
Dimple magnetic drain plugs in all compartments.