Can I use the words 'respect' and 'deference' interchangeably?
Yes, respect and deference can be used somewhat interchangeably if the person to whom you accord respect is the same person to whom you accord deference. In other words, respect and deference can go together like a horse and carriage.
If, however, you do not respect a person, deference may simply be the proper and diplomatic thing to evince, despite one's lack of respect for the person.
Commenter @TimRomano said it well, when he said,
You can defer to people you do not respect, and respect people to whom you do not defer.
The following sentence illustrates the difference between the two words:
Although I did not respect the winner of the election, I gave him his due deference when we began working together.
Although I did not give the winner of the election his due deference, I at least gave him my respect when we began working together.
On the other hand, we have:
Since the winning candidate was my best friend, my respect for him quite naturally made me more than happy to give him his due deference.
Since the winning candidate was my best friend, my deference to him quite naturally made me more than happy to give him his due respect.
In conclusion, the two words are not necessarily interchangeable, but they can be in some instances. When respect for a person is lacking or is given grudgingly, deference to him or her may also be given grudgingly, if only to keep up appearances.