My argument is not that no traits will be important to your identity, but that the list of which traits are will be dependent upon someone's own personal experience.
Ultimately, I think it fair to reason that we are defined by those traits which are most distinguishable within our community. (Hence, the use of those traits to differentiate ourselves from others, and vice versa.) However, which traits count as distinguishable will vary from community to community. My point with the example of "being 5'6"" not being a defining trait is that that is a very average height - most people are around that height, so they will probably experience very little treatment related specifically to it.
But, people who are very short or very tall most likely do have unique experiences related to being particularly short or tall, and so it would be reasonable for them to define themselves, in part, as being short or tall.
I myself have grown up with very little importance placed on sexuality, receiving very little to no discrimination or differentiation because I am gay. (Arguably, I am all the more fortunate for this.) As a result, I have never felt defined by it.
Other people, however, have had very unfortunate experiences related to being gay, where their community has made a point to differentiate them based on that factor. To them it is perfectly reasonable and understandable that they should then define themselves by their sexuality, for undoubtedly those experiences (particular to their sexual orientation) will have helped define their character.
