Respect--may no longer be the right word to characterize teams or franchises. Teams rise and fall. Some teams don't quite fall as far as others; same is true about rising.
A better word, a more descriptive word might be "prestige or prestigious."
The presence of Shula and Robbie created a franchise that became something special. It took years for that "prestige" to melt away. It began when Jimmie Johnson replaced Shula and our prestige started to really plummet with that big loss that ended Johnson's and Marino's career. It spiraled out of control and hit rock bottom when the team went 1-15. Parcells, et al, did little to regain anything. It was clearly evident when the Dolphins were not able to secure any noteworthy coach to replace bumbling Sparano that our prestige was gone.
We are ignored. Our franchise is in the "has been" category today. Winning is the only way back to regaining it. Winning the division, getting through the playoffs and getting into the SB would put us back on the map. The ownership has to present themselves better too.