One of the key points of a debate is to listen to your opponent's arguments and refute them. A debater who's able to do this not only shows respect to his/her opponent but also proves to be much more mature; after all, it's just a debate, and unless there's something big at stake, there's no reason not to show respect.
Being respectful in a debate gets you far, because not only does your opponent (and any watchers) gain respect for you, you also might have a much more fun debate.
Respect in a debate is key because it shows value for the other person and keeps the debate fun for everyone. Insults derail the conversation and do not foster good argumentation. Respect maintains good discussion because it prevents the environment from becoming unsafe to be in. Even if you are close-minded on a topic, as long as you are respectful, you can have a great debate during which everyone has fun.
Respect is important, no doubt. Without respect, a debate would be a bunch of people just yelling at each other... Kind of like Congress. However, open-mindedness is the most important thing to have in a debate. How can a debate ever end if no one is willing to look at the facts and possibly leave their own beliefs behind?
First off, let me say that any given person's ideas are not necessarily deserving of respect. Having said that, the people generally are. However, when it comes to a debate, respect must take a back seat to reasoned arguments and evidence. Unless the disrespect gets to a point where it detracts from one's ability to follow the arguments, it should really be a non-factor.