Which international organizations would Texas join?

The ones a functioning nation needs to trade, fly, ship, and cooperate with its neighbors, and Texas would move on them quickly. Joining international bodies is routine administrative work that every new country does, not a gauntlet, and most of these organizations exist precisely to bring sovereign states into common systems.

Start close to home: the Organization of American States

A natural early step, and one the movement has named, is the Organization of American States. Its charter, signed at Bogota in 1948, commits its members to peace and security in the hemisphere, "the pacific settlement of disputes," and "common action in the event of aggression." Its membership rule is simple: "All American States that ratify the present Charter are Members of the Organization." For a new nation in the Americas, the OAS functions as a cooperation and non-aggression framework with its neighbors, exactly the kind of standing a Texas would want from the start.

The bodies that keep the country running internationally

Beyond the OAS, a short list of technical organizations does the unglamorous work that lets a country operate across borders. The International Civil Aviation Organization sets the rules that let your flights land in other countries; its membership is open to sovereign states, and joining is how an independent Texas plugs its airports into the global aviation system. The International Maritime Organization does the equivalent for shipping, which matters enormously for a state with the busiest ports in the union. The Universal Postal Union connects national mail systems so a letter crosses borders. These are intergovernmental clubs of states, and a new state joins them as a matter of course.

The trade system

To trade on stable, predictable terms with the wider world, a country accedes to the World Trade Organization. We cover the mechanics in the trade-agreements answer, but the short version is that the WTO is open to "any State or separate customs territory possessing full autonomy in the conduct of its external commercial relations," on terms negotiated with the membership. Texas, with the 8th-largest economy on earth and exports to more than 200 countries, is precisely the kind of trading economy the system is built to include.

Finance and development bodies, as Texas chooses

A new nation can also take its place in the international financial institutions, the kind that handle currency stability, cross-border payments, and development finance. Whether and how Texas engages with each is a sovereign choice for the future Texas government, weighed against Texas's own considerable financial strength. The point is that the door is open. Membership in the world's economic institutions is available to any serious economy, and Texas is one of the most serious on the planet.

These are decisions for a free Texas, and that is the point

Which specific organizations Texas prioritizes, on what timeline, and on what terms, are exactly the kinds of choices that belong to the elected government of an independent Texas, not to a movement pre-writing the future. What can be said now is that none of these doors are closed to Texas, that joining is normal administrative work, and that an economy of Texas's size is welcomed into these systems rather than kept out of them.

The bottom line

Texas would join the bodies a nation needs: the OAS close to home for hemispheric cooperation, the aviation, maritime, and postal organizations to keep travel and commerce moving, and the trade system to lock in stable terms with the world. These are routine memberships open to sovereign states, and a free Texas would decide the specifics for itself.