I really have a difficult time understanding why this topic generates such heated debates (not to suggest that this particular debate has become heated). As Gabriel writes, just because one person cannot see differences in the signatures of different lenses, it does not follow that those differences are not present. Conversely, just because one person can see the characteristics or behaviours that distinguish different lens signatures, it does not follow that these differences are or should be significant for everyone.
I think there is a perception held by many for whom lens signature is less apparent or less important that when individuals express a preference for a particular lens signature they are in fact asserting the superiority of their own judgment. In one sense their judgment is superior. In another it is not. In order to comprehend this distinction, we must understand that there are different types of judgment at play in the assessment of photographs.
The first type of judgment rests on experience and is developed through practice. There can be no doubting the fact that experience plays into one's capacity to differentiate different lens signatures. It should be perfectly obvious that those who have spent more time using and studying the behaviours of different lenses will be more able to differentiate them on the subtle points that constitute signature. This is not to say that everyone who has been a photographer for many years will develop this ability. Not all photographers study the nuances of lens signature. And there is absolutely no requirement that photographers must do so in order to be brilliant or even halfway decent at their craft. The study of lens signature is a point of focus that appeals (for any number of reasons) to some and less to others. Now certainly there will be those who will refine this type of judgment much more quickly and easily than others. But we must recognise that this type of judgment rests entirely upon experience. Nobody can distinguish the signature of a Sonnar from that of a Planar if he or she has no previous experience with one or both.
The second type of judgment is subjective aesthetic judgment. And, though this form of judgment can be refined through experience, it does not rely on experience. For example, the very first time that I see a painting of any sort, I am able to determine whether or not I like it. Now, after viewing more paintings, I may revise my intial judgment of the first painting. I might, for example, conclude that I like it, but not as much as this other one. But the essential point here is that this form of aesthetic judgment does not rely on experience.
The problem in many of these debates about lens signature, as I perceive it, is that many for whom lens signatures are less important or less apparent interpret others' expressions of preference for a particular lens signature as an expression of the superiority of their powers of judgment in the second sense. If you accept what I have written above, it should be clear that such an expression of superiority would be untenable. It should also be clear just how unlikely it would be that someone asserting their preference for a particular lens signature over another would possibly be asserting the superiority of their judgment in this second sense.
To make this point differently, I offer my own experience as a past downhill ski racer. Even to the uninitiated, a downhill ski race is often very exciting. But those who have spent years training and studying technique will usually be better able to point out subtle differences in the styles of different skiers and in their performances. I can see mistakes, moments of greatness, bold moves and chances taken that would likely elude the perception of those who have less experience with this sport. This fact does not, however, suggest that a ski race will be any more exciting for me than it will be for others. And it does not imply my superiority in any way that is not perfectly justified. I have spent countless hours (years actually) training for this sport. So it stands to reason that I will be better able to explain why a particular skier had a better run than another. But my judgment of the excitement and the thrill of the race is no better than that of a person who is out watching their very first race. We are both equally, though differently, able to assess whether or not we enjoyed the race, found it exciting, et cetera, et cetera, et cetera.
We all take photographs for our own reasons. We all have our own visions and our own aesthetic preferences. But some have spent more time studying the subtleties and nuances that distinguish the behaviours of different lenses. Their judgment is no better or worse in the second (subjective) sense. But it is better in the first (objective) sense. They can see differences that others cannot because they have devoted sufficient time and energy to studying them.
Does this matter? It does in some circumstances and does not in others. If you have a lens that renders images in ways that are pleasing to you then it does not matter whether or not you can explain how this lens is different from another. If you have several lenses that give you results that you consider to be indistinguishable from one another but that all meet your standards and expectations then, again, it does not matter if someone else does see a difference between the behaviours of these lenses. In neither of these cases is your ability to excel at photography in any way diminished by your inability to distinguish the signatures of different lenses.
The only instance in which an individual's limited capacity for judgment (in the first sense) is significant is when he or she is dissatisfied with the look of his or her photographs and yet cannot explain why. If this is your situation, if you find yourself unable to make photographs that have the look that you want them to have, then your limited capacity to judge different lens signatures is significant. But there is good news. This type of judgment is not innate. It is learned. It can be developed through study.
To those out there who feel affronted by others' expressions of preference for different lens signatures, ask yourself a question: Do I want the ability to differentiate different lens signatures? If the answer is yes then devote the necessary time and energy to studying the behaviour of different lenses. If the answer is no then let it go. Your powers of aesthetic judgment are in no way challenged by another's assertion of preference for a particular lens signature over another. And the temptation to present yourself as the child in the "Emperor's New Clothes" should be strongly resisted.