Short answer. Not under the willful disobedience ground in Article 282, which specifically requires disobedience of a lawful order given in connection with his work. An instruction unrelated to your actual duties does not fit that description, though the employer could still try to justify dismissal under a different just cause depending on the facts.
What the law says
Termination by employer. An employer may terminate an employment for any of the following causes: Serious misconduct or willful disobedience by the employee of the lawful orders of his employer or representative in connection with his work; Gross and habitual neglect by the employee of his duties; Fraud or willful breach by the employee of the trust reposed in him by his employer or duly authorized representative; Commission of a crime or offense by the employee against the person of his employer or any immediate member of his family or his duly authorized representatives; and Other causes analogous to the foregoing.
Labor Code, Article 282 — Just Causes For Dismissal. Read the full provision →
The connection to your work is part of the statutory text
Article 282 lists serious misconduct or willful disobedience by the employee of the lawful orders of his employer or representative in connection with his work as a just cause. The phrase 'in connection with his work' is not incidental; it limits the clause to orders that relate to the employee's actual job. An instruction that has nothing to do with the duties an employee was engaged to perform sits outside the plain language of this ground.
The order also has to be lawful
Beyond the work-connection requirement, the order disobeyed must be lawful. This is a separate condition from relevance to the job: even an order connected to your work does not satisfy this clause if the order itself is not lawful. Both conditions, lawfulness and connection to the work, have to be present for refusal of that order to fit within willful disobedience as this article defines it.
Refusing an unrelated order does not end the inquiry entirely
Falling outside the willful disobedience clause does not necessarily mean dismissal is impossible on some other basis. Article 282 also lists gross and habitual neglect of duties, fraud or willful breach of trust, commission of a crime against the employer or specified persons, and other causes analogous to the foregoing. Whether a refusal to follow an unrelated order could be evaluated under one of those other grounds depends entirely on the specific facts, which this article's text does not address in the abstract.
What remains unresolved by the bare text
Article 282 does not define where the line sits between an order that is 'in connection with' your work and one that is not, nor does it address borderline instructions that touch on workplace conduct generally without being tied to a specific job duty. Those line-drawing questions depend on the particular job and the particular instruction, something the statute leaves to be worked out rather than settling in advance.