"I will give you a new heart and put a new spirit in you; I will remove from you your heart of stone and give you a heart of flesh." - Ezekiel 36:26
Calvinists interpret it as Israel being totally depraved and God stating that He will irresistibly change someone's will. But I've always interpreted it as God changing a person's heart in the sense of, say, for example, God takes someone who's greedy and makes them charitable. Or He takes someone who's full of hate and changes them (by their request of course) into a heart that's loving. Or taking a heart full of lust and God cleanses the thoughts of that person. It's basically bringing about a change in a person after they've freely chosen to repent and receive The Holy Spirit into their hearts. That's the way I interpreted it (long before I eve knew of the Calvinism/Arminianism debate). When a person repents and turns to Jesus, he asks Him to sanctify him, to help him become a better person. So, if a person is uncaring or unloving (having a heart of stone), Jesus helps them to become the opposite of that (He gives them a heart of flesh). In context, this is what Yahweh is telling Israel He will do to them if they repent and turn to Him in repentence. He's saying that He'll make them into better people than they were before.
Of course, even if this interpretation were false, that says nothing about supporting the T.U.L.I.P theology. Ezekiel 36:26 may just be simultaneously expressing Total Depravity and Prevenient Grace/Resistible Grace. Even we Arminians believe human beings cannot turn to Christ unless The Father draws on us by His Holy Spirit (see John 6:44 and John 6:65). In our natural state, we are haters of God and His ways. We cannot turn to Him in repentance in the absence of The Holy Spirit. The Holy Spirit is the means by which we come to Christ, bow our knees to Him and are saved. The Holy Spirit is kind of like a life preserver that the captain of the ship (God) throws to a person who has fallen overboard. Without the life preserver, there's no way a person can get back onto the ship. He can't swim! He'll just flail about and drown! However, we believe that The Lord gives this enabling grace to everyone. We believe that The Holy Spirit tries to persuade a person to turn to Him their entire lives up until the point of death OR until the person becomes so hardened that repentance is no longer possible without overriding the free will (Romans 1:24). In our life preserver analogy, it would be like the Captain pleading with the person who fell overboard to grab onto the life preserver that he freely offers but, in his pride, tries to save himself. Perhaps he hates the captain for some reason and doesn't want to be in debited to him for saving his life. He flips the bird at the captain and tries to work his way back onto the ship (by attempting to swim toward and trying to climb up the side of the ship and whatnot). He ends up drowning despite the captain's best efforts to persuade him to do otherwise.Some of the people who fell overboard were finally persuaded and freely chose to go in the direction of the life preserver while others resisted his offer to the very end.
Ezekiel 36:26 may be stating that human beings can't respond on their own and that\ Jesus will enable them to repent by extending His grace. Or it could mean that Jesus will exchange their negative personality traits with ones more in line with his commandments (e.g unforgiveness for forgiveness, greed for selflessness, etc.). Either interpretation is completely in line with Arminian theology.