I applied for a job but was not given the chance for an interview due to a relative working for the same company. They considered this a "conflict of interest" though I can prove relatives have worked together in the company before.
Even the job description does not match up to why they are considering this a conflict of interest.
Employment / Labor Attorney
Generally yes, an employer can restrict family members from working together at the same company. An employer generally can also enforce that rule selectively so long as the reason for the selective enforcement is not an unlawful one. Unlawful reasons would include (but not limited to) race, sex, disability, age (over 40), religion, national origin and ethnicity. If the employer refused to consider you for a job based on the conflict of interest but really made the decision not to consider you for an unlawful reason then the conflict of interest reason is an excuse for an unlawful motivation and certainly you would have some remedies at law against the employer. If you believe this is the case then you should talk to an employment lawyer ASAP because there is a short time period in which you must start prosecuting claims against the employer.
You cannot sue an employer for being stupid. (Can you imagine the number of lawsuits?)
An employer is free to hire anyone they want and be inconsistent with their polices, so long as they are not doing for for an illegal reason, such as racial discrimination.
Unless you have evidence of an illegal reason, you do not have a claim. Sorry.