Questions re his origins arose long before he produced the birth cert and suspicion grew when he didnt do so sooner.
Obama released his short form birth certificate in June 2008, before he was even elected. The policy of the state of Hawaii was to provide computer-generated certificates, which of course fuelled the fire. The original long form was released in April 2011. By then there was every incentive for the Obama White House to let various Republicans discredit themselves by endorsing what had become a mass delusion on the right wing of the political spectrum.
Would you accuse Chileans or Iranians or various other 3rd world LEO of anti-americanism or racism for putting CIA/America on a list of who'd benefit by orchestrating false flag stunts in overthrowing their democratically elected govts back then?
Your question seems to confuse historical facts with hypothetical possibilities. It is well known that the CIA aided coups in Iran and Chile during the 1950s and 1970s respectively. The CIA was rather notorious for engaging in often amateurish direct action in this era, e.g. the Bay of Pigs.
Since the mid-1970s, however, increased congressional and senate oversight along with a shift towards electronics intelligence and away from human intelligence make it less probable that any
new accusation of CIA malfeasance is actually true. This does not rule out the possibility but it makes it less likely.
Moreover, from the mid-1970s direct actions have been more frequently carried out by US special forces, e.g. the failed attempt to free the Teheran hostages in 1980, or the apprehension of Osama Bin Laden, in both cases certainly with CIA support, but not the work of "the CIA".
Seeing the hand of the CIA in everything that might possibly be construed as bad would indeed be a sign of anti-Americanism, but there's a big difference between a rational suspicion of foreign interference in a conflict, and a kneejerk accusation, such as Hugo Chavez
claiming that multiple Latin American leaders were victims of a US "cancer plot". Chavez was previously nearly ousted in a coup in 2002, and despite earlier denials then changed his tune to say later on that the US was involved, even though
the evidence indicates the opposite.
Iran made anti-American noises for decades after the overthrow of the Shah in 1979, and backed up the rhetoric with actions, e.g. the hostages crisis in the first years of Khomeini's rule. In recent decades Iranian leaders have tended not to provoke the US directly but have made their feelings rather plain about Israel, especially under Ahmadinejad.
Thus when bad things happen to Iranian nuclear scienists it is perfectly rational to assume that Israel (and thus Mossad) may indeed have been responsible, since there is a very overt conflict there. Israel struggled unsuccessfully against the US-brokered deal over nuclear power with Iran. There was a lot of sabre-rattling from Israel and its supporters elsewhere, and since they had previously attacked an Iraqi nuclear plant to derail a potential nuclear weapons program, everyone including the US took them seriously.
However, for years there were conspiracists claiming that the US was imminently about to attack Iraq, echoed at various times by mainstream media comments from kneejerk anti-American writers. Yet the Obama administration was actually working quietly behind the scenes to broker a deal with Iran. Today, the two countries are cooperating to a certain extent against ISIS, in an enemy-of-my-enemy scenario.
Suppose some LEO put Mossad/Israel govt on a list of "Who would benefit from 911?" ....How anti-semitic is that?
Law enforcement, i.e. the FBI, traced the identities of the 9/11 hijackers within 72 hours, revealing that most were from Saudi Arabia with a few Egyptians, Lebanese and UAE citizens mixed in.
Since the WTC had previously been attacked by Al-Qaeda, it seems very unlikely that any law enforcement officer would have had cause to brainstorm possible culprits by resorting to 'cui bono'.
Had one done so and fingered Mossad then the chance would be indeed quite good that the LEO was an antisemite, for the simple reason that even moderately geopolitically informed investigators (i.e. anyone who reads the foreign news sections of quality newspapers) would know that Israel was and is a US ally, with no known reason then or now to orchestrate a massive terrorist strike on its chief sponsor.
For the same reason, if the LEO had fingered the United Kingdom in this unnecessary hypothetical brainstorming exercise on September 11-13, then the probability would be overwhelming that the investigator was a deranged Anglophobe.