Would Texas be a republic or a democracy?

A republic, the same form Texas has now. The Texas Constitution does not merely allow a republican form of government, it requires one, and that requirement is the one limit written directly into the people's power to change their own government.

Texas is already a constitutional republic

A republic means the people govern through elected representatives under a constitution and the rule of law, rather than deciding every question by direct majority show of hands. That is exactly what Texas is today. Texans elect lawmakers, an executive, and judges, all bound by a written constitution and a Bill of Rights. Independence does not change that character. It carries it forward, with the same elections and the same representative institutions, now answerable to Texans alone.

The republican form is locked into Texas law

This is not a preference. It is a constitutional commitment. Article 1, Section 2 of the Texas Constitution states that the faith of the people of Texas stands pledged to the preservation of a republican form of government, and that, subject to this limitation only, the people have at all times the inalienable right to alter, reform, or abolish their government as they think expedient. Read that carefully. The one and only limit Texans placed on their own sweeping right of self-government is that whatever they build must stay a republic. That guardrail does not disappear at independence. It is part of the document Texas carries with it.

Why the republican form is a feature, not a technicality

A republic protects against two opposite dangers at once: the concentration of power in one ruler, and the raw, unchecked will of a momentary majority. Representatives, a written constitution, separated powers, and a Bill of Rights all slow things down and force decisions through institutions that answer to the people over time. That is how the rights of every Texan, including those on the losing side of any given vote, stay protected no matter which way the political winds blow.

Where the people still rule directly

None of this means Texans are kept at arm's length from the big questions. The decision on independence itself is made by the people, directly, through a referendum, the most democratic instrument there is. A republic uses direct votes of the people for the foundational choices and elected representatives for the day-to-day work of governing. Independent Texas would keep both, exactly as the framework already provides.

The bottom line

Texas is a republic now and would remain one, because its own constitution requires it. The people decide the great questions directly and govern through elected representatives the rest of the time. Self-government, under the rule of law, with the rights of every Texan protected.