Under the scenario reported at Taxgirl website, Texas would not protect these whistle blowers. In this case, filed in Oklahoma, two accoutants reported to their boss, a charity, that the charity (Feed the Children) owed back taxes for several years. The employer was so happy to learn about the mistake that she fired the two truth tellers.
I cannot speak to Oklahoma law, but in Texas, such conduct is not protected by law. We, as private sector employees, are not protected for honestly blowing the whistle, whether we blow it to our boss or to some law enforcement agency.
In Texas, if your employer tells you or instructs you to commit an illegal act and you refuse, then you have some protection. But, to simply report either up the chain of command or to some law enforcement agency that the employer is violating the law, then you have no protection.
There is a new federal statute, the Sarbanes-Oxley Act, that offers protection for private sector employees who report fraud committed by a publicly traded company (inspired by the Enron collapse). But, even this statute would not apply to employees of the typical charity.