Would an employee in a government company that follows Western systems, which are contrary to Sharia, be sinful, and is his salary lawful?

If the employee does not directly commit what is forbidden, nor assists in it, then there is no objection. Otherwise, it is not permissible, due to the generality of Allah's saying: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression." An example of what is forbidden is usurious dealings, selling or drinking alcohol, or assisting in them. It does not matter if the perpetrators are disbelievers, because they are addressed by the subsidiary rulings of Islamic law, according to the preponderant opinion.