I understand where your coworkers are coming from. Getting the application up and running to prove the concepts the application intends to solve is critical in a business setting. If you can implement search by hitting every element in the array in a fraction of the time it would take to implement a binary search, you are that much further along to seeing the application in action.

If they actually refuse to go back and implement a better algorithm once the characteristics of the application are known, that is another matter. Do these people actually hold the same beliefs once they start to see the performance of their application rapidly degrade?