Since the prophet decrees that you kill all non Muslims they are not correct they are in fact lying.
Only during a time of war when they are are fighting against muslims.
Otherwise, it is absolutely fine to live with and around non muslims.
But the quran also says, do not take them as friends, or marry them.
I see on the news that muslims are carrying sighns that say behead those that insult the prophet(pooh) Here are the verses that inspire muslims to cut off people's heads.
8.12 Remember thy Lord inspired the angels (with the message): "I am withyou: give firmness to the Believers: I will instil terror into the hearts of the Unbelievers: smite ye above their necks and smite all their finger-tips off them."
47.4 Therefore, when ye meet the Unbelievers (in fight), smite at their necks; At length, when ye have thoroughly subdued them, bind a bond firmly (on them): thereafter (is the time for) either generosity or ransom: Until the war lays down its burdens. Thus (are ye commanded): but if it had been God's Will, He could certainly have exacted retribution from them (Himself); but (He lets you fight) in order to test you, some with others. But those who are slain in the Way of God,- He will never let their deeds be lost.
Here is a verse that says do not marry unbelievers.
2.221 Do not marry unbelieving women (idolaters), until they believe: A slave woman who believes is better than an unbelieving woman, even though she allures you. Nor marry (your girls) to unbelievers until they believe: A man slave who believes is better than an unbeliever, even though he allures you. Unbelievers do (but) beckon you to the Fire. But God beckons by His Grace to the Garden (of bliss) and
forgiveness, and makes His Signs clear to mankind: That they may celebrate His praise.