Show us where in the text God gave in to Moses. That's right, you added that in there and is nowhere to be found. God said he shows mercy to whom he wills.
Your problem here is the normal one, not understanding that when non-Calvinists disagree with Calvinism, they are not arguing against God; they are arguing against the Calvinistic understanding of God. The two are very different.
People’s eternal destinies are not the subject of God’s statements in Exodus 33.
4 When the people heard these distressing words, they began to mourn and no one put on any ornaments. 5 For the Lord had said to Moses, “Tell the Israelites, ‘You are a stiff-necked people. If I were to go with you even for a moment, I might destroy you. Now take off your ornaments and I will decide what to do with you.’...
12 Moses said to the Lord, “You have been telling me, ‘Lead these people,’ but you have not let me know whom you will send with me. You have said, ‘I know you by name and you have found favor with me.’ 13 If you are pleased with me, teach me your ways so I may know you and continue to find favor with you. Remember that this nation is your people.”
14 The Lord replied, “My Presence will go with you, and I will give you rest.”
15 Then Moses said to him, “If your Presence does not go with us, do not send us up from here. 16 How will anyone know that you are pleased with me and with your people unless you go with us? What else will distinguish me and your people from all the other people on the face of the earth?”
17 And the Lord said to Moses, “I will do the very thing you have asked, because I am pleased with you and I know you by name.”
God has become frustrated with the sinful and rebellious ways of His people, Israel. While Moses is on Mount Sinai with God, the people have made for themselves a golden calf to worship (Exodus 32:1-6). This event sets off a debate between God and Moses about what God should do to the people of Israel in response to their idolatry.
Moses returns the people of Israel, and rebukes them for their behavior (Exodus 32:15-29). They repent, and so Moses returns to speak with God and plead with Him to forgive the people (Exodus 32:30-32). God says He will forgive them, but that He will not go with them to the Promised Land because His holiness would consume them in their sin (Exodus 32:33–33:6).
Moses, however, continued to intercede with God for the people of Israel. He tells God that if God does not go with them to the Promised Land, then they should not go at all (Exodus 33:12-16). Finally, God agrees to go with the Israelites to the Promised Land, as Moses has requested (Exodus 33:17).
It is extremely ironic that a verse which Calvinists use to tell people not to disagree with God is found in a context in which Moses is doing exactly that.
Yes, God exerts His right to be gracious and compassionate to whom He wants, but He is not talking about determining people’s eternal destinies; He is talking His right to bestow blessings and favor upon certain people for certain reasons. In this case, God decided, as a result of His friendship with Moses, to bless Moses with a special revelation of Himself.
"The whole context of these words, then, is not one of some despotic puppeteer, who predetermines everything and applies “might is right” principles. It is of a loving personal God, interacting with and answering the prayer of a person in faith-relationship with him, but reminding the person that God knows best how and to whom to distribute blessing." (Marston and Forster, God’s Strategy in Human History, 60).
Exodus 33:19 does not teach us that we should not question God’s actions because “God is God and He can do what He wants.”
Far from it! Exodus 33:19 teaches exactly the opposite. It is stated at the end of a very long debate between God and Moses about God’s plans for the people of Israel. At the end of this discussion, God shows Moses that He has no desire to kill and destroy His people, for His character is centered on mercy and compassion.