能力のある三公・摂政・関白が高齢だといえども辞めてはならない
I understand everything in this except for だといえども, and I'm kind of struggling to find a good explanation of what it means. Anyone have any ideas?
いえども is a formal / fancy (and archaic) way of saying 言{い}っても. So だといえども = だといっても. A sentence like 「XXXだといっても」 could parse out to "so even if you're saying that XXX, ..."
The -ど verb ending is very old in Japanese, appearing in the Kojiki and the Man'yōshū, some of the earliest writing ever in the Japanese language. It attaches to the 已然形{いぜんけい} or realis form, and is used to introduce a contrary position, much like the English "but". In some ways, the realis is used a bit like the subjunctive in English and German (and maybe other European languages too?) -- it attaches to ば for conditionals: "if that be the case...", and it attaches to ど for contrary conditions: "although that be the case...". The ど ending isn't used much in modern Japanese, outside of a few set expressions like いえども.
There is one word in modern Japanese where you do see this ど a lot: けど, and its longer formal form けれども. There are several theories for the origins of けれども, but they all agree that this is the realis form of something plus ども, which itself is this classical ど + も.
In classical Japanese, just remember that this attaches to the 已然形 (usually the stem form ending in an -e sound), and it basically means "but, although, however".