In other words, why do the British have the Falklands, Jamaica, etc etc as part of the common wealth or territories? For example, they did not put up with Spanish and with any Soviet interference (I understand that is a big leap considering the Cold War and the "Domino Effect")
TL;DR: The Monroe Doctrine said that the United States opposed any European power colonizing any already independent state in the Americas, but expressly did not apply to areas that had been colonies and remained as such.
There is an old US State Department page saved in the Wayback Machine. It's from Monroe's message to Congress of 2 December 1823. The important words:
... declare that we should consider any attempt on their part to extend their system to any portion of this hemisphere as dangerous to our peace and safety. With the existing colonies or dependencies of any European power we have not interfered and shall not interfere. But with the Governments who have declared their independence and maintained it, and whose independence we have, on great consideration and on just principles, acknowledged, we could not view any interposition for the purpose of oppressing them, or controlling in any other manner their destiny, by any European power in any other light than as the manifestation of an unfriendly disposition toward the United States.
The UK has continued possession of the Falklands, Anguilla, Bermuda, the Cayman Islands, Montserrat, and Turks and Caicos Islands, and the US had never recognized the independence of any of them, so they fall under the "existing colonies or dependencies" part, just like the various (later) provinces of Canada, British Guyana, British Honduras, Bahamas, et cetera, were not violations in their time.
"The United States established diplomatic relations with Jamaica in 1962 following its independence from the United Kingdom." The constitutional position of some countries that the Queen is the head of state is apparently considered a trivial survival (and if the US didn't consider it so, then it would still remain under the "existing colonies or dependencies" part).
Similarly for France's continued possesion of Saint Pierre and Miquelon, French Guyana, the French West Indies. And for the Netherlands' continued possession of Aruba, Curaçao, S. Maarten, Bonaire, Saba, and S. Eustatius.
Similarly for Spain's continued possession of Cuba and Puerto Rico, until the Spanish-American War, of which I know little.