Are students able to "opt-out" of standardized tests in Texas public schools?

No. State law makes it clear that students may not opt-out of tests, including standardized tests. The complete Texas Education Code section 26.010 states:

EXEMPTION FROM INSTRUCTION. (a) A parent is entitled to remove the parent’s child temporarily from a class or other school activity that conflicts with the parent’s religious or moral beliefs if the parent presents or delivers to the teacher of the parent’s child a written statement authorizing the removal of the child from the class or other school activity. A parent is not entitled to remove the parent’s child from a class or other school activity to avoid a test or to prevent the child from taking a subject for an entire semester.

(b) This section does not exempt a child from satisfying grade level or graduation requirements in a manner acceptable to the school district and the agency.