What happens if some countries recognize Texas and others refuse?

Texas functions as a nation regardless, because under international law a state exists by meeting the criteria, not by collecting unanimous approval. Partial recognition is common, it is workable, and over time self-interest tends to close the gap.

Recognition does not have to be unanimous to be real

This is the heart of it. A country is not a country only once every other government agrees. The declaratory theory of statehood, the prevailing view in international law and written into Article 3 of the Montevideo Convention, holds that "the political existence of the state is independent of recognition by the other states." A state that meets the criteria, a population, a territory, a government, and the capacity to conduct relations, is a state. Recognition formalizes relationships; it does not switch existence on and off. So a Texas recognized by many and not yet by a few is still, in law and in fact, a nation.

Partial recognition is a normal condition, not a crisis

Plenty of states in the world today are recognized by large numbers of countries and not by certain others, and they govern, trade, and conduct diplomacy all the same. Recognition is decided one government at a time, and governments weigh their own politics and interests, so a perfectly even result is rare. What matters is reaching the threshold where enough key states and the major international institutions deal with you as a country. Past that point, a holdout's refusal is a statement about the holdout, not a veto on your nationhood.

The functioning nation accumulates recognition over time

Recognition is not frozen at the moment of independence. It builds. As a new nation governs effectively, honors its commitments, and trades reliably, more governments find it in their interest to formalize relations, and earlier refusals soften. Self-interest is patient but persistent: the longer Texas operates as a stable, prosperous country, the weaker the case for any government to keep pretending otherwise. The gap tends to close, not widen.

Economic weight does the persuading

For Texas specifically, the incentive to recognize is unusually strong. This is the 8th-largest economy on earth, a top energy producer, an exporter to economies on every continent. A government that refuses to recognize Texas is choosing to complicate its own access to Texas energy, Texas goods, and Texas markets. That is a cost a holdout pays, not Texas. Over time, the pull of dealing with a major economy works steadily in the direction of recognition, because the alternative is self-imposed exclusion.

Practical life continues throughout

While recognition accumulates, the country runs. Texas would govern its territory, run its economy, manage its border, conduct trade under world trade rules, and deal directly with the many governments that have recognized it. Citizens live, businesses operate, goods flow. The existence of a holdout somewhere does not stop the mail, the ports, or the markets. The functioning of a nation is the strongest argument for its recognition, and Texas would be functioning from the start.

The bottom line

Texas exists and functions as a nation once it meets the criteria and enough key states and institutions deal with it as one, whether or not every government has signed on. Partial recognition is a normal, workable condition, the gap closes over time as self-interest accumulates, and the pull of the world's 8th-largest economy works steadily in Texas's favor.