What is the ruling on creating social media applications like Instagram and Twitter for someone when the creator knows that they will be used for an evil purpose, and what should one do if this request causes them embarrassment?

If it is highly probable that a person asking you to create a social media account will use it for impermissible acts, then you are not allowed to help them. This is because doing so would constitute aiding in sin and transgression, which is forbidden in Islamic law, as Allah Almighty says: "And do not cooperate in sin and aggression." Ibn Taymiyyah mentioned that assisting in disobedience is forbidden, and he cited as evidence the Prophet's (peace be upon him) cursing of ten individuals involved with intoxicants, and the prohibition of selling weapons to someone who will use them for unlawful fighting. You must apologize to him, and if you do not fear a greater harm, then inform him frankly of the reason; perhaps that will deter him from disobedience.