First, we should note that democracy does not automatically mean that we will show no deference whatsoever to members of the governing class. We do not address the President as "Barack." Instead, we call him "Mr. President." So democracy and deference are not incompatible.
What explains this is that deference is given to those who have earned it, not those who somehow claim it on the basis of their birth. This is the real difference between colonial American society and British society. In America, there was deference, but it was deference to the wealthy who had presumably earned the right to be deferred to, not deference to the high-born who demanded deference because of who their family was.
So, democracy and deference are compatible so long as the deference is paid to people based on their accomplishments and not on their pedigrees.