I have read personal stories from tall women about some of their dating troubles. A common* complaint by these women is how the men they wish to date are either intimidated by them or somehow "feel less manly" in their presence. I find the behaviour of such men bizarre and, more accurately, sexist.
Whenever I have been in the presence of a woman equal to me* in height or taller, I have never felt any hostility or fear towards her for being a tall woman. I've met plenty of people — men and women — taller than I am. Have they ever made me nervous? Certainly...back when I was I child, but even then I considered a tall person's gender irrelevant.
I think that many men who are freaked out by tall women are misogynists. The only reason a man could feel uncomfortable around a tall woman is because he perceives her to be a threat to his self-given "authority" or ability to bully her into conceding an argument to him by using his size advantage as a weapon. Any man who believes this or thinks that a tall woman would reduce his masculinity cannot be considered a man: he is a coward.
Even if he isn't a misogynist, a man of average or above average height bothered by tall women should put everything into perspective: how does a short woman feel when she has to interact with a man who is at least a foot higher than her? If the man intended to cause her harm it is unlikely she would be unable to stop him, but when it comes to a man and a woman of equal height, in most cases the man would still be physically stronger than the woman. Therefore, a man has no reason to feel insecure or threatened by tall women.
For the ultimate question, would I go out with a woman near my height or taller? My answer: Yes — why not? I'm not intimidated by tall women, I don't have a need or desire to control women or engage in one-upmanship over them (same goes for men) and I would not
have any problem with being the shorter person in a
relationship. I've observed taller woman/shorter man
relationships before and I am happy for the people involved in them.
Men should not be insecure about tall women — or about women in general, for that matter — and nor should they only be romantically interested in shorter women purely to maintain a physical advantage in a relationship. All women, regardless of their stature, are entitled to basic respect.
 Some tall women prefer to date even taller men, and thus, limit their dating pool as a result. However, this post exclusively addresses male sexism.
 I am six feet tall and have met women taller than this.