The Thai monarchy, a revered institution shielded from criticism by a strict lèse-majesté law, has traditionally been seen as above the political fray, although royals have intervened in moments of political crisis.
I wonder whether any member of the British royal family has ever been a candidate for Prime Minister in the UK? It is well known that the Queen (or King) is supposed to be (or seen as) neutral in political affairs. But what about other royal members? I can't find anything on the Wikipedia page dedicated to the monarchy of the UK.