The question seems to imply (perhaps for dramatic effect) that Objectivists know about something called a "9/11 Truth movement," and that it would be puzzling for knowledgeable Objectivists not to endorse it. But the basic philosophical perspective of Objectivism is well stated in the answers already posted by Greg and someone code-named "sector7agent." Objectivists are moved by evidence -- demonstrable facts of reality. The question as asked merely offers assertions with no attempt to offer any references that can be checked for confirmatory or refutory evidence.
Ordinarily it would not be the responsiblity of independent observers to search for evidence to support wild assertions. In this particular case, however, I did a little basic searching on the Internet. I was quite surprised to find a fairly detailed article on exactly the topic of "9/11 Truth movement" on Wikipedia. Evidently there is stronger support for alternative explanations of the 9/11 events than I had previously known, although the kind of evidence alluded to in the Wikipedia article still does not seem to integrate very well with so much other evidence that would be well known to those who lived through the events of 9/11/01. Typically conspiracy theories such as what the question suggests wait a little longer to surface. Nine years is a little short. There are still too many people around who can remember what they themselves saw and heard on that day and the days and weeks that followed.
The question asserts:
Nearly all objectivists have accepted this official account and base their foreign policy positions on it, as well as ignore the intensified infringement of rights in the name of the war on terrorism.
This claim is utterly false. Influential Objectivists have long advocated strong action against Iran, based on 50 years of history as well as the 9/11 attacks, and have repeatedly blasted the government's attempt to fight terrorism by infringing the rights of Americans at home.
The question further asserts:
That the official 9/11 conspiracy theory is largely false is easily exposed by an evidence-based investigation of the perceptual evidence (e.g., the manner of the WTC towers' destruction) and the analysis of the government's conduct during the attacks (e.g., the stand-down of the air defences).
My own recollection of the 9/11 event and public reaction to it is that the American public would have been willing to go to all out war in response to the attack, if the U.S. government, along with prominent politicians and the media, hadn't gone into high gear to defuse the public's outrage. The stand-down of air defenses was merely an act of timidity on the part of the government, out of fear of public repercussions if a commercial aircraft filled with American passengers had been shot out of the sky precipitously. The government was simply and woefully unprepared for such an occurrence, as far as I recall. Governments in many countries, including the U.S., did at least ground all commercial air traffic for a substantial length of time as the attacks were unfolding, and Air Force One went promptly airborne to protect the President and facilitate his abiilty to direct the government's further responses.
Objectivists, perhaps more than others, are normally willing to follow evidence wherever it leads. If there really is clear evidence of anything other than a conspiracy by militant Islamic warmongers who found a way to demolish the seven-building World Trade Center with two commercial airliners used as flying bombs, let's hear it. (The other five buildings, as I recall, were too badly damaged by debris from the collapsing Twin Towers to remain standing after about seven hours or so.)
As an engineer myself (though not a mechanical or structural engineer), one particularly intriguing avenue of potential evidence is the claim by some apparent engineers that the two buildings hit directly by the airliners could not have collapsed in the way they did without clandestine assistance (referred to in the Wikipedia article as "controlled demolition"). I recall watching a documentary TV program years ago about the technical aspects of the collapses, explaining that the heat from the fireball of blazing jet fuel, injected deep into the internal structure of the building, could have weakened the lateral steel supports enough so that, after an hour or so, they were no longer strong enough to hold the building together against the weight of all the floors above the point of impact.
Even if there is merit in the "external assist" or "controlled demolition" engineering argument, however, it still fails to integrate very well with other facts. If, for example, demolition explosives had been planted in the two towers, when could that have been done? It seems doubtful that it could have happened after the impacts, with so many hundreds of police, fire and rescue personnel swarming all over the Trade Center Complex to rescue as many victims as possible from the burning floors and above those floors (and eventually being trapped and killed themselves as the towers collapsed). If the explosives had been planted before the morning of the attack, then whoever did it would have to have known that the attack was coming. Who, besides more terrorists, could have known that? Who, besides terrorists, would have had any reason to do nothing to head off the attack, or to detonate the alleged explosives?
The Wikipedia article suggests one hypothesis that the U.S. Government could have been responsible for such a thing, allegedly in furtherance of some vague "oil conspiracy," i.e., the Bush Administration allegedly in cohoots with "Big Oil." Come on! That is really just too fantastic to have any credibility at all.
The question mentions appeals to 9/11 to justify the invasion of Iraq. That's another point that doesn't integrate. The 9/11 terrorists had no direct connection to Iraq, and the Bush Administration knew it. The case against Iraq was based on nuclear non-proliferation, not retaliation for 9/11. At the same time, the Bush Administration certainly also tried to project itself to the American people as taking strong and decisive action against teror by invading Iraq. That was a pathetically flimsy connection to promulgate and was criticized as such by prominent Objectivists at the time. Objectivists who spoke out publicly were busy advocating action against Iran, not Iraq, and Iran continues to be a key focal point for Objectivist observers to this day.
Your basic framing isn't credible because Objectivists are demonstrably loud and persistent advocates of pursuing truth everywhere and in everything (see your 2nd paragraph and my answer, for example). And that they indeed live by this principle is evidenced by their holding to many and varied ideas fundamentally at odds with those of the culture at large. So to be credible in your basic framing, you need to provide a reference with evidence that most (heck, even some) Objectivists are indifferent to the truth in this context. Or you could perhaps change it to point to the real issue.
And do you have some sort of reference to substantiate your assertion that Objectivists "ignore the intensified infringement of rights in the war on terrorism"? Every Objectivist I know, including myself, is keenly aware of this and of course objects to it.