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.

Yes, it is required by various state and federal laws: https://tea.texas.gov/sites/default/files/state-and-federal-required-tests.pdf

Yes. Students are subject to compulsory attendance and may commit the offense of failure to attend school, and a parent may commit the offense of contributing to nonattendance if the student fails to attend school. (Texas Education Code §§ 25.093, .094)

Makeup Tests: It is important to note that missing school on a single designated test date will not necessarily cause the student to have missed his or her testing opportunity. Most tests are administered from a testing “window” set by TEA. If a student who has been absent returns to school during the testing window, he or she may be asked to sit for the exam at that time. Makeup test dates that extend beyond the test window are in place for most STAAR tests.

Yes. Students are encouraged to do their best on a testing day but are not required to complete the test. All eligible students present at school on a test date must be included in the test administration. Campus officials are required to submit a test score code for every student, in accordance with TEA test administration guidelines.

There are implications regarding required accelerated instruction, along with graduation requirements.

Under TEC §28.0213, a school district must also offer an intensive program of instruction to a student who does not perform satisfactorily on any state assessment instrument administered under TEC Subchapter B, Chapter 39. In addition, a recent amendment to the statute now requires that intensive instruction be provided to a student who is not likely to receive a high school diploma before the fifth school year following the student’s enrollment in grade nine, as determined by the school district.

HB4545 requires Accelerated Instruction for any student who did not pass STAAR grades 3-8 or EOC assessments. There are specific guidelines addressed in the legislation. A student who did not take an assessment would be required to fulfill the HB4545 accelerated instruction components.

High School Graduation: Students must pass the five end-of-course exams or an acceptable substitute in order to graduate, as described above. By local policy, a school district may issue a certificate of coursework completion to a student who successfully completes curriculum requirements but who fails required state assessment tests. Texas Education Code §§28.025(d).

Texas Association of School Boards - Opting Out of Standardized Tests