Would there still be political parties?

That is for Texans to decide, and almost certainly yes, because free people organize. The movement takes no side on which parties should exist or who should win. What can be said is that independence is not a partisan project, and the party landscape of an independent Texas belongs to its voters, not to this movement.

Independence is not a one-party cause

Texas independence is not the property of any party. The case for it, that decisions about Texas should be made in Texas by Texans, lands across the political spectrum. Support is broad enough that it does not fit a single partisan box, and a cause that wide cannot be the project of one faction. The movement's discipline here is deliberate: it advocates for self-government and takes no stance on the partisan questions a free Texas will settle for itself.

Parties are how free people organize

In every free republic, people who share goals form parties to contest elections and offer voters a clear choice. There is no reason to expect that to stop in an independent Texas, and no desire to stop it. Whatever parties exist would do what parties always do: compete for votes, advance their ideas, and answer to the public at the ballot box. The right to organize politically is itself one of the freedoms self-government protects.

The field could open up, not close down

There is a practical reason an independent Texas might see a livelier political landscape, not a narrower one. Today, money and attention flow toward Washington, and incumbents draw on contributions from across the union. Once Texas governs itself, that out-of-state money is foreign money, and Texas does not allow political contributions from foreign sources. The result is a more level field, more room for new voices and real competition, and more turnover when voters want it. That tends to widen the political conversation rather than wall it off.

The choices belong to the voters

How many parties, which parties, how they nominate candidates, how elections are organized around them, all of that is for the people of Texas and their elected representatives to decide. The Texas Nationalist Movement does not endorse candidates and does not pick partisan winners. It works to put the decision in the hands of Texans and trusts them to run their own politics.

The bottom line

Yes, almost certainly there would be political parties, because free people organize, but the shape of that politics is for Texas voters to decide. Independence hands the people a more level field and gets out of the way.