Christians are not libertarians, but I will answer the question anyway. You asked if God gave the same grace to all, but where does God give the same grace to all? Why assume that? Rather, God's grace is sufficient for all to have the free choice. You asked why do some believe and some do not? Because they have been given the free choice as sovereign free willed human beings made in His image. God has provided them with the best world ensemble possible yet in that world most still reject God with the free choice to do so.

This is right where the Calvinist gets stuck because instead of accept God does something we can't understand how He does it, he has to try to get into God's mind and make rules for God that go contrary to His mind. The Calvinist in doing so has no humility and is trying to get ahead of God's mind when God has not given you the ability to understand how He does some things. Can you accept this God?

Since salvation is not by works then it is not more or less works why a person is saved and another is not. Since a person can't will themselves into being saved as Calvinists try to do by assuming they were irresistibly selected then that is not the reason why a few are saved and most are not. Though it can be said that is why a Calvinist is not saved because he refuses to genuinely search God out with all his heart and soul to receive the gift of repentance and faith to be regenerated.

You keep arguing against libertarian free will, but Christians don't believe in libertarian free will so why carry on like that as though we do? That's sinning bearing false witness. OSAS Arminians believe not in libertarian free will but sovereign free will made in God's image. He has provided total provision for and is within His divine providence and allowance. This is something your god can't do so God trumps your god every time! Praise the Lord! Hallelujah!