It's likely for legal liability reasons. There's a reason why people (especially women) feel more comfortable going to a doctor of the same sex. There's a reason why bathrooms are segregated by sex in this country as well.
I certainly understand your point and it's nice to see people not hung up on gender, but it's rather impossible to tell someone's sexual orientation and indeed some people are attracted to both sexes.
Having someone patted down by someone of the same sex greatly reduces the likely hood of any sort of issue caused by a complaint by the TSA officer or the person being search.
In terms of people's comments on sexual arousal, I was patted down last week. It's not invasive and unless the TSA starts hiring supermodels, there's not much stimulation to it.
In terms of the gender neutrality, I think they do this in Europe as well from what I recall. They're not nearly as crazy and repressed about sex as people are in the United States.
If TSA doesn't respect its own rules or the Constitution, do you really think it would respect gender identity?
If the rules violated the constitution then someone would sue and the rather conservative court would overturn the rules. Nobody has been able to prove that anything you're talking about is against the constitution. You sort of forgot to mention that in your argument so I thought I'd help out.
Does the TSA respect my right to determine my own gender identity?
They likely do. Why don't you ask next time.