Would Texas issue its own passports?

Yes. Issuing passports is one of the basic functions every independent nation performs, and an independent Texas would do it like any other country. A Texas passport is part of what it means to be a nation among nations, and the movement has named it as a concrete step in securing independence.

A passport is standard nation-state machinery

Every sovereign country issues travel documents to its citizens. It is as routine as running a treasury or a court system. A passport is simply a government's certification of who its citizens are, recognized by other governments so its people can travel. An independent Texas issuing Texas passports is not exotic or aspirational; it is one of the ordinary, expected functions of statehood, and the plan for securing independence lists it plainly alongside reopening a Texas embassy abroad.

Texas already runs the kind of identity systems this requires

Issuing secure documents is not new ground for Texas. The state already operates large-scale identity and credentialing systems, issuing driver licenses and state IDs to tens of millions of people with security features, biometric data, and verification built in. The institutional muscle to produce a secure, internationally recognized travel document already exists in Texas. Standing up passport issuance is a matter of organizing capability the state already has, not inventing it from nothing.

It would meet international standards so it works everywhere

For a passport to be useful, other countries have to accept it, and that runs through the same global system every nation uses. Travel documents follow international standards set through the civil-aviation framework that nations join, which is how a passport issued in one country is read and trusted at a border in another. As covered in the international cluster, an independent Texas would join those bodies as a matter of routine administrative work. A Texas passport would be built to that standard, so it functions at borders and airports around the world.

The design and the rules are Texas's to set

What a Texas passport looks like, what it costs, how citizens apply, and the rules around it are decisions for the future Texas government, not things the movement pre-writes. That is the honest answer, and it is the right one: these are sovereign choices for a free Texas to make. What is certain now is that Texas would issue passports, that it has the capability to do so, and that those documents would carry the recognition a functioning nation's passport carries.

Until then, travel keeps working

Issuing a new passport does not mean Texans are stranded in the meantime. The vast majority of Texans who hold US passports keep them, because Texas independence does not strip US citizenship, and managed travel between Texas and its neighbors is handled the way contiguous countries handle it. See the answers on passports to the US and freedom of movement. The Texas passport is an addition to a Texan's options, not a hoop to clear before anyone can move.

The bottom line

Yes, an independent Texas would issue its own passports, built to international standards and recognized abroad, using identity systems the state already runs. The specifics are for a free Texas to decide, and the plan to secure independence already names the Texas passport as a step.