As a native speaker, I think 我是长头发 isn't grammatically correct. People can understand it, but it's still wrong grammar. I never say/write anything like this. You are not a piece of hair but a human/man/woman/kid/student/worker etc. I think a lot of native speakers make similar mistake like this (using something that are not supposed to describe a human to describe a human).

As a native speaker, I think 我是长头发 isn't grammatically correct. People may use it in oral speech, but it's still incorrect grammar. I never say/write anything like this. You are not a piece of hair but a human/man/woman/kid/student/worker etc. 

I think a lot of native speakers make similar mistake like this (using something that are not supposed to describe a human to describe a human). This could be debatable, even to me it's clearly wrong. Why don't you say 'my hair is long' or 我的头发很长 to avoid this usage?