It seems that there are two strands to this discussion:
roles that take on the sex of the actor playing them (eg, The Leading Player, the Cat in the Hat)
roles that are played by both sexes but are fixed character-wise (eg, Lady Bracknell has been played by male and female actors but the character is always a woman)
"You travel alone because other people are only there to remind you how much that hook hurts that we all bit down on. Wait for that one day we can bite free and get back out there in space where we belong, sail back over water, over skies, into space, the hook finally out of our mouths and we wander back out there in space spawning to other planets never to return hurrah to earth and we'll look back and can't even see these lives here anymore. Only the taste of blood to remind us we ever existed. The earth is small. We're gone. We're dead. We're safe."
-John Guare, Landscape of the Body