Does the law that prohibits refusing to sell, display advertisements, or provide a service to customers, and punishes those who refuse, prevent working in the field of advertising, limiting it only to those who do not care about what is permissible and what is forbidden?

Working in and profiting from the field of advertising is permissible, subject to its Sharia-compliant regulations. The fact that an employee is obligated to deal with a client seeking a forbidden service does not prohibit it, as long as the forbidden aspect does not dominate. If one is commanded to do something forbidden, obedience is not obligatory, and one can evade it, based on the Prophet’s (peace be upon him) sayings: "Obedience is only in what is good and right," and "There is no obedience to a creature in disobedience to the Creator." If one cannot evade it and fears unbearable harm, then the sin falls upon the one who compelled them.