Lee Salem writes:
It's frustrating to see the "pilot" episodes without "The Contest" in sequence.
Sequentially, it should come after "The Outing," I believe. There is a very humorous scene in "The Contest" which shows George visiting Estelle in the hospital and a gorgeous nurse coming in to give a beautiful female patient a sponge bath. George gets aroused watching their shadows through the curtain in much the same uncomfortable way he reacted to the male nurse giving a male patient a sponge bath in "The Outing."
You've got the connection right but the order wrong. The female/female bathing scene comes first (in The Contest), then the male/male bathing scene comes next (in The Outing).
(Although why Estelle should be assigned to a room with a male patient is anyone's guess.)
She shares a room with a male patient because the writers wanted to make a parallel hospital bathing joke. This is, in fact, your biggest clue that the male/male scene comes second in the sequence. In the first bathing scene, the setup is logical because it's derived from the plot of the episode. In the second bathing scene, the setup is illogical because it's derived from the plot of a different episode, and wedged into a new episode.