A couple of things:

• You're starting from the assumption that the American government didn't feel as if they were blindsided by the French and British actions. They were.

• Second, it ran counter to the narrative that the Eisenhower Administration was trying to push on the International stage. The Hungarian Revolution was happening at the same time and the US wasn't going to sound very credible if it condemned the Soviet intervention but not the French & UK intervention...which dovetails to my first point.

So overall, did he do the right thing?

He was still hoping he could keep the Egyptians out of the Soviet Camp, that summer the Egyptian government had decided to go with a Soviet aid plan for infrastructure construction(specifically the Aswan Dam) but in the months and years ahead of that it appeared as if the US was going to come to an agreement for technical aid. Ike made a gamble that all was not let lost.

Were France and Britain clearly in the wrong for wanting to protect their interests?

I'd say that the British and French could not have picked a worse time(during the Soviet intervention in Hungary), from a international "moral high ground" standpoint.

Can someone ELI5 why Eisenhower did not back his Western allies, the UK and France, over the Suez Canal?

To answer that, we need some background: The Suez Canal had been contructed 1859-1869 by the French, who had obtained the concession for 99 years from the viceroy of Egypt and Sudan. His successor sold Egypt's shares to Britain and in 1888, the Convention of Constantinople declared the canal a neutral zone under the protection of the British. Ownership and upkeep remained by the Suez Canal Company. This was reconfirmed under the Anglo-Egyptian Treaty of 1936.

In the 1950ies, Arab nationalism rose. The maybe most prominent Arab leader was Gamal Abdel Nasser of Egypt. Both the Soviet Union and the US had interests in securing Nasser's allegiance: The Soviets, to gain control over the oil reserves and shipping lanes of the Near East, the US and its allies to prevent that.

In Nasser's eyes, British control over Egyptian soil was a huge offence, even though Britain had agreed to withdraw its military from Egypt in 1954 and the last British troops left in June 1956. Nasser also sought to modernize Egypt, e.g. through the building of the huge Aswan Dam. For that, he needed funds. The US and Britain were willing to provide financial aid, however when Nasser started to co-operate with the Soviets and bought huge amounts of weapons from them, the US and Britain withdrew from the agreement. Nasser also strove to create a pan-Arab Union.

Breaking the 1936 treaty and successfully expropriating the Suez Canal Company before the concession would have run out in 1968 meant a source of income with which to support Nassers's industrialisation projects. Moreover, defeating a European colonial power would also bestow huge prestige on him and thus aid his plans of unifying the Arabs under his leadership. So, on July 26, 1956, Nasser declared the nationalisation of the Canal.

For the British, Nasser had been growing problem; not only had he interfered with the operation of the Canal, but also undermined British influence in the entire region. So, they secretly negotiated the Protocol of Sèvres with the French and the Israelis. The goal was to reassert control over the Canal and to oust Nasser. The French joined because Nasser had been sponsoring the anti-French rebellion in Algeria. The Israelis had been suffering under Nasser closing both the Canal as well as the Straits of Tiran to Israeli shipping, and blockading the Gulf of Aqaba, thus cutting off the Israeli port of Eilat.

In October 29, 1956, the Israeli Forces started Operation Kadesh in the Sinai and defeated the Egyptian forces in 100 hours, capturing the entire Sinai peninsula and stopping just 10 miles short of the Canal. On November 1st, French and British planes destroyed the Egyptian air force and gained air superiority. On November 5, French and British forces landed in Port Said, at the entrance of the Canal, and secured the city two days later.

So, why did the US backstab its allies? US foreign policy under Eisenhower and Dulles saw French and particular British influence in the region as a huge obstacle against winning over the Arab nations and keeping the Soviets out. The clash of interests had already become apparent at the Buraimi Dispute, where Britain had sided with their own protegée (Oman) instead of the American one (Saudi Arabia). So, Washington isolated France and Britain diplomatically at the UN and threatened to dump the US Government’s Sterling Bond holdings if Britain didn't end the invasion and withdraw its troops. So, Britain was forceed by the US to withdraw on December 1st.

So overall, did Eisenhower do the right thing?

In so far as he replaced European influence over the Middle East with US influence and kept the Soviets out: Clearly yes.

Were France and Britain clearly in the wrong for wanting to protect their interests?

IMHO history doesn't answer moral questions.

Sources:

[1] Anthony Gorst, Lewis Johnman: The Suez Crisis. Routledge, New York 1997 - ISBN 0415114497

[2] Simon C Smith: Reassessing Suez 1956: New Perspectives on the Crisis and its Aftermath. Ashgate, Aldershot 2008 - ISBN 9780754661702