Have I committed a sin by refusing to deal with a person who is hostile towards Islam and belongs to a racist ideology, until he changes the content of his page that expresses this?

You did not err in what you did with this person, because what motivated you was your zeal for the religion and your hatred for falsehood, and what became apparent to you was his defiance of Allah and his display of enmity towards Islam. In such a situation, wisdom dictates severity towards such people, and gentle speech is not suitable for them, in affirmation of the Almighty's saying: "And do not dispute with the People of the Scripture except in the best manner possible, except for those who wrong among them."

However, it is not permissible for a Muslim to engage in dialogue with disbelievers regarding their doubts without knowledge that enables him to refute falsehoods and clarify the truth. A Muslim's mercy extends to defiant disbelievers, motivating him to invite them to Allah with insight and patience in enduring their harm, in order to save them from the Fire. This is the fundamental principle in dealing with them, in affirmation of the Almighty's saying: "And be patient over what they say and depart from them with a gracious departure."

If a Muslim invites to Allah with knowledge and wisdom, clarifies the correct viewpoint, and fulfills the right of advice, then he will not be harmed thereafter by his words being rejected or mocked. And the ignorance of the ignorant should not lead him away from the etiquette of Islam in inviting to Allah Almighty.