What is the authenticity of the Hadith: "Every Jew or Christian who hears of me and does not believe in me before he dies will be admitted by Allah into the Fire on the Day of Resurrection"? Does the warning of entering the Fire include everyone who has been reached by Islam but does not believe in it?

The Hadith, "Whoever among my Ummah, or a Jew, or a Christian hears of me and does not believe in me, will not enter Paradise," is authentic. It is incumbent upon a Muslim to convey the religion. Whoever refrains from conveying it has disobeyed Allah and His Messenger, and has deprived people of good. Their entry into Hellfire, in that case, would be due to their rejection of the truth, not due to its conveyance to them.