If you committed fraud by signing a customers name to an order without permission that sounds like grounds to terminate you. Other people in the company doing the same wrong is not a valid defense. If the customers in those instances were unhappy with the orders they would have defenses against the fees they owed in those circumstances.
Your only defense would be if you were ordered to do this by your superiors, and even so it is not much of a defense to fraud.
Every legal matter is fact specific, and there are often nuances in every case. This is intended for comment only, and does not create an attorney client relationship.
Texas is a right to work state. Typically, unless an employee has an employment contract, or is employed under a collective bargaining agreement through a union, the employer can modify or terminate the employment at any time with or without cause. If an employer, at any time, decides they no longer want to employ someone, for any non-discriminatory reason, that employee can legally be terminated. However, an employer generally cannot terminate an employee for prohibited discriminatory reasons (such as racial discrimination), or in retaliation for certain protected actions (such as whistle-blowing). What you describe does not sound like prohibited discrimination or retaliation. Just because other people do things they shouldn't doesn't mean you cannot be terminated.
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TX is an at will state, which means that the employer can fire you for any reason, so long as it is not discriminatory in nature or in violation of an employment contract (if such a contract exists). Having said that, the mere fact that others within the Company are engaging in a prohibited act does not relieve you for doing so. If the Company terminated you for a violation of their policy then they may have good cause; and this would not be considered discriminatory in nature. However, the Company should be applying consistent disciplinary measures for all of its employees.
Rengin Bekhtyar's answer to a legal question on Avvo does not establish an attorney-client relationship.