But I'm only confirming what God's word says. His word, not ours.
Read Matthew 7:21-23, which speaks of those who professed to be christians, but were never actually IN Christ. They were christians by title only, never truly saved.
And non believers do have zeal. Paul mentions Israel here. Just one example...
Romans 10:1-13: "Brethren, my heart’s desire and prayer to God for Israel is that they may be saved. For I bear them witness that they have a zeal for God, but not according to knowledge. For they being ignorant of God’s righteousness, and seeking to establish their own righteousness, have not submitted to the righteousness of God. For Christ is the end of the law for righteousness to everyone who believes. For Moses writes about the righteousness which is of the law, “The man who does those things shall live by them." But the righteousness of faith speaks in this way, “Do not say in your heart, ‘Who will ascend into heaven?’” (that is, to bring Christ down from above) or, “‘Who will descend into the abyss?’” (that is, to bring Christ up from the dead). But what does it say? “The word is near you, in your mouth and in your heart” (that is, the word of faith which we preach): that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved. For with the heart one believes unto righteousness, and with the mouth confession is made unto salvation. For the Scripture says, “Whoever believes on Him will not be put to shame.” For there is no distinction between Jew and Greek, for the same Lord over all is rich to all who call upon Him. For “whoever calls on the name of the Lord shall be saved.”