What is the proper etiquette with regard to someone trying to get to their
seat in a theater? Should you stand up? Should you move your legs to one
side to allow them to pass? Should you assess the patron who is trying to
pass to see if they have the capability to pass without you adjusting
yourself? Are they old? Infirm? Overweight? Should your demeanor change
once the house lights are down and the show is about to begin?

Ellen

Proper etiquette dictates that you should stand up when someone tries to get to their seat. In almost every case, especially in old Broadway houses, rows are so narrow that standing up is the only way to avoid someone crawling over you to get to his seat.

Although this rule seems to work fine before the curtain has gone up, Ask Gothamist would add that if you are in the rare theater that offers ample leg room and the performace has already started, you should not stand. (This might be more of an option in newer movie theaters with stadium seating.) The more people who stand to accommodate one late person, the greater the disturbance to the people in the rest of the theater, especially those sitting behind your row.

If you are the person who is late to a performance and need to get to your seat, Emily Post advises that you face the stage as you make your way down the row. Why? She offers no real reason, but Ask Gothamist thinks it has to do with a certain respect for the actors - having your back to them would be rude - and the fact that the people in the row in front of yours probably don't want your butt brushing up against their heads as you find your seat.