Is it permissible to show bias towards a Muslim when appointing someone or to prefer them with a higher salary, even if they are less experienced or competent than a non-Muslim, in a job that requires choosing the most qualified person to achieve the company's interests?

The agent is obligated to act in the best interest of his principal. If the company does not stipulate Islam for its employees, then the inquirer should choose the most competent, most experienced, and lowest-paid individual, even if they are not Muslim, as long as the nature of the work does not necessitate it.