Normally, the employer is permitted to implement and enforce such a rule, as long as they pay the employees from the time they are required to report to work, even if a half hour before their shift begins.
Since other employees are held to the same standard, that would typically indicate that discrimination is not playing a role in the employer's decision.
However, because you are aware of other employees who were not minorities who engaged in more severe violations and received less severe punishment, I would normally pursue a grievance based on race discrimination, seeking to have the same level of punishment for the same offense as non-minorities.
It could make a difference between keeping or losing your job if you were late during the 18 month period.
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