The cheers that rang across the hall of the Unesco meeting when Palestine became a member on Monday are being echoed in surprising quarters.

The Obama administration has perversely given a big boost to the Republican right's antipathy to the UN and all it stands for. Ironically, it was George W Bush who brought the United States back into Unesco 20 years after Reagan withdrew. Equally ironically, driving the engine in this diplomatic train wreck was Barack Obama, whose speeches in Turkey and Egypt during the early months of his presidency had deceptively signalled a new opening to the Muslim world.

By reflexively withdrawing from Unesco in response to Palestine's admission, the Obama-Clinton state department has taken the lunatic fringe and put them centre stage. Representative Ileana Ros-Lehtinen, a Florida Republican who chairs the House foreign affairs committee, combines a Likudnik support of Israel with a recidivist hatred of the UN and has been trying to de-fund the UN and its agencies.

In contrast, Hillary Clinton, who visited Unesco's Paris HQ earlier this year, had announced: "I am proud to be the first secretary of state from the United States ever to come to Unesco, and I come because I believe strongly in your mission." Indeed. So strongly does she believe in it that she is prepared to pull out of the organisation for recognising the Palestinian statehood that Obama had himself called for at the UN general assembly in September 2010.

The voting lineup on Monday was indicative. France, much more diplomatically adroit than the US, and mindful of its global standing, supported Palestinian membership. Even subservient Britain could not bring itself to vote with the US and pusillanimously abstained. The voting suggests that when the security council resolution on Palestinian UN membership comes up next week, it will get the nine affirmative votes needed – which means the US will have to use its veto and risk consequences, such as those threatened by the Saudis.

If the US had put nearly as much pressure on Israel as it had on others to avoid using its threatened veto, it would be a much more credible and creditable world power. As it is, its desperate attempts to avoid a veto by getting others to do its dirty work for it have made the Obama administration look like a toddler who hides his head behind the curtains and cannot understand why everyone can still see him.

The security council vote apart, the Unesco vote presages Palestinian admission to other agencies. One looks forward to US withdrawal from the International Atomic Energy Agency, relieving the pressure in Iran, or from the World Health Organisation, as soon as Palestine is allowed to join.

Compounding the irony, Israel itself has so far not indicated it is pulling out of Unesco, nor indeed any other UN agency. On the contrary, WikiLeaks recently revealed that Israel was angling for a major position in Unesco.

The nature of the US approach is clear. There is a general lack of principle. For example, the route being followed by Palestine in its effort to join multilateral institutions replicates that of the Vatican, whose far more dubious claim to statehood derives from its original membership of the Universal Postal Union, since the postage stamp-sized enclave did indeed issue its own stamps.

The actual legislation the state department invokes is a 1990 prohibition on funding "the United Nations or any specialised agency thereof which accords the Palestine Liberation Organisation the same standing as a member state", and another in 1994 banning payments to "any affiliated organisation of the United Nations which grants full membership as a state to any organisation or group that does not have the internationally recognised attributes of statehood".

Any president, as we have seen, has ways to get around congressional mandates like this. For example, there are questions about which manifestation of Palestine is applying: the PLO or the Palestinian Authority. The congressional legislation was passed before the Oslo accords – and before the US began funding the Palestinians directly, so an executive decision could have declared that events had overtaken the intent of the law, and, what is more, that it was not the PLO but the Palestinian state that had been admitted.

As for the second part, US diplomats will have fun explaining why the US maintains membership of the World Bank and IMF – which have admitted Kosovo, whose disputed territory and statehood, rightly or wrongly, has far less general recognition than Palestine's.

The White House should listen to the cheers in the hall that followed the Unesco vote – reminiscent of those that greeted the end of another period of diplomatic folly when Beijing took Chiang Kai-Shek's seat in the UN after decades of American pretence that an off-shore island represented China there.

Over-stretched financially and militarily, beset with problems that can only be solved multilaterally, doing Binyamin Netanyahu's bidding will win Obama few votes at home. The American Likudniks will still believe the president is an alien-born Muslim and send their votes and cheques accordingly. Abroad, the US has abandoned all logic, all signs of joined-up diplomacy, and abandoned the last vestiges of pretensions to be an honest broker in the Middle East.

As an epitaph to American diplomacy and illusions of empire, look at the votes for Palestine: Afghanistan, Iraq, Kuwait and Libya all voted against the US. Any more candidates for liberation?