The first problem in answering the question is that the term “sexual orientation” has a number of closely related but distinct meanings. At least three come to mind: sexual orientation as a scientific concept, sexual orientation as a legal concept, and sexual orientation as social concept.
Sexual orientation as a scientific concept
As I understand the current research, what “sexual orientation” is measuring and how useful a concept it is remain open questions. What is sexual orientation a measure of? How should it be operationally defined? Is sexual orientation in men the same thing as sexual orientation in women? Should sexual orientation include all of the factors involved in a person’s pattern of sexual attraction (e.g. personality features, physical features, etc.) or be limited to the part gender plays in their sexual attraction? Is "sexual attraction" more about a person's patterns of sexual attraction or about patterns of sexual arousal? Are heterosexuality, homosexuality, and bisexuality each somehow unified groups in some scientifically important way or are they just conglomerations of merely superficially similar features lumped together? These remain open questions, and they probably will for some time.
Sexual orientation as a legal concept:
In anti-discrimination legislation, often involving employment and housing, the difficult scientific question are simply irrelevant. In the Employment Non-Discrimination Act (ENDA), currently under consideration in the US House of Representaitives, it defines sexual orientation as follows: "The term `sexual orientation' means homosexuality, heterosexuality, or bisexuality." What the prohibits is as follows:
(a) Employer Practices- It shall be an unlawful employment practice for an employer--It's very important that it says "actual or percieved" sexual orientation or gender identity.
(1) to fail or refuse to hire or to discharge any individual, or otherwise discriminate against any individual with respect to the compensation, terms, conditions, or privileges of employment of the individual, because of such individual's actual or perceived sexual orientation or gender identity; or
(2) to limit, segregate, or classify the employees or applicants for employment of the employer in any way that would deprive or tend to deprive any individual of employment or otherwise adversely affect the status of the individual as an employee, because of such individual's actual or perceived sexual orientation or gender identity.
Suppose that a law said that it is illegal to discriminate against someone on the basis of their sexual orientation (without saying anything about “actual or perceived”); this would create the potential for a very undesirable loophole: it might be legal to discriminate against someone on the basis of believing that they’re belong to one of the LGBT categories as long as they aren’t actually LGBT. Consider the following hypothetical example. Employee X and employee Y work at the same company, and Y particularly dislikes X. Now, X is a heterosexual male, but he’s single and doesn’t date much. Y, knowing their boss to be particularly homophobic, spreads a rumor around the workplace that X is gay. On the basis of this rumor, the boss fires X. If the law says that you can’t discriminate against someone on the basis of their sexual orientation, the boss has probably not violated it. X is heterosexual and was not discriminated against on the basis of his sexual orientation. Moreover, this loophole could then create a situation where the employer could try to argue that the employee who was fired on the belief that they are LGBT isn’t actually LGBT. To counter this, people would have to try to prove in court what their sexual oriention or gender identity actually is, which could require putting in the public record very personal information, and the very idea that this is something people might have to try to “prove” in court would be exasperating to many. Both of these would be highly undesirable situations. I assume it is to avoid them that the law says, “actual or perceived.” That means, discriminating against people (in employment, and possibly housing, depending on the law) on the basis of a belief about their sexual orientation is wrong, regardless of whether that belief turns out to be correct or not.
In sexual orientation as a scientific concept, questions of operational definitions in research (how to measure what a person’s sexual orientation is) are extraordinarily important. In sexual orientation as a legal concept, not do operational definitions not matter, in many cases, what a person’s sexual orientation actually is does not matter.
Sexual orientation as a social concept
This is probably the most important part of the idea of sexual orientation; it’s also the hardest to define or explain. Basically, I’m including here popular ideas about sexual orientation, knowing that there is a diverse range. In terms of sexual orientation as a social category, the scientific questions above aren’t that important, although what people think the science often is important in how people think about the matter. Legal issues are also rather far from most people’s minds. But I think it is clear that the general idea(s) about what sexual orientation is that are floating around the general population are quite a bit different than the other two types. And it’s primarily these that inform how people use “sexual orientation” to think about themselves and others.
When looking at things this way, I think it becomes clear why asking whether asexuality is a sexual orientation becomes a more complicated question than it might seem at first: Which definition of “sexual orientation” do we have in mind? The isues involved in each case are not identical.