Michael Stravato for The New York TimesThe Republic of Texas settled in Overton in 2003 after acquiring an old hospital to serve as a capitol. OVERTON, Tex. - The road to the capitol winds through a landscape of pine trees, rusting pump jacks and a few tidy churches in this East Texas town. Literature in the lobby describes how citizens can apply for passports or enlist in the interim defense forces. The building is the headquarters of the Republic of Texas, a sometimes militant organization whose members repudiate the authority of Austin and Washington and believe Texas should be...