Can a 17-year-old legally move out of her parents' house and marry her 20-year-old boyfriend without her parents' permission in Texas?

A 17-year-old can not get married in Texas without parental consent unless they have court approval. That's going to be hard to get if your parents object and your only reason is because "we don't want to wait another year until I'm 18".

As far as moving out, anyone under the age of 18 is a minor and therefore under the control and authority of their parents, which means the parents decide where you live. There is a big difference between moving out on your own (into your own place and fully supporting yourself) and moving in with a boyfriend. I'm willing to bet that if your parents scream loudly enough about it, then they can get something done. For example, Texas has laws that cover: Enticing a child (intent to interfere with the lawful custody of a child younger than 18), Harboring runaway child (knowingly harboring a child who is younger than 18 and who is voluntarily absent from their home without the consent of their parent or guardian for a substantial length of time or without the intent to return), Interference with rights of guardian of the person (takes, retains, or conceals a ward when the person knows that by doing so it interferes with the right of a guardian of the person to have physical possession of a ward and to establish the ward's legal domicile).

But, I'm not an attorney.