Fransknorge, I beg to differ with you. I posted the european law and I have been asked to show my disability card several times in multiple european countries. But not for early boarding on an airplane. But to take my PTST dog into "no dog" areas.
But also note your post is specific re; "rights of disabled persons and persons with reduced mobility when traveling by air" If you plan on taking a service dog on an European Airplane, they will ask to see your disability card. I speak from experience