I feel the word' celebrity' would be more accurate than 'rank.' Certainly rank counts in the military. It is laid down both traditionally and in standing orders that the higher the rank, the more respect is to be shown by those of lower rank, e.g. privates respect (or should) senior sergeants. Lower ranking servicemen defer and treat (generally out of fear of reprisal) captain and colonels with a sort of reverence. And Generals and Admirals...well...it is hard for a lower deck sailor or a buck private soldier to even meet one.
People often take note of what they see on the media and tend to hero worship those who are deemed to be famous, or rich, or powerful, or who have an amazing talent and are often in the news (Celebrity) But this sort of deference varies enormously from country to country. Here in Australia it is fairly low and it is not that unusual for the average man or woman to call his or her boss, or even the 'head honcho' of a big firm by their first name. This would be unheard of in many European countries.
It is quite possible to respect another person without regarding them as your inferior or superior. The proviso is you see them as a human being and not in the current role they are playing...whatever that might be.