Calvinism rejects libertarian free will and believes in compatible moral freedom, which means everything and everyone is micro-determined. The following are the definitions of the two perspectives.
Determinism and moral responsibility are compatible; hence, the name. This compatibility is not achieved by compatibilism being less deterministic than hard determinism. Rather, it is achieved by defining free choice to mean as long as a person chooses according to his greatest desire, he can be considered to have made a free choice for which he is morally responsible; even though given the same past, he cannot choose differently in the moral moment of decision.
Consequently, the difference between compatibilism (soft determinism) and hard determinism is not to be found in the levels of the deterministic nature of each because they are the same. Rather, the difference is compatibilism contends people are morally responsible for their choices if they are made according to their greatest desire, and hard determinism says they are not.
Therefore, moral responsibility is the product of defining free choice as a person acting in accordance with his greatest desire even though the desire is determined. I frequently find Calvinists who affirm soft determinism and disavow hard determinism because they think soft determinism is not as unflinchingly deterministic as hard determinism. That kind of thinking is based upon a misunderstanding of compatibilism.
Man is not determined. He has the actual ability to choose between accessible options, at least in some scenarios. Libertarians contend determinism is not compatible with moral responsibility. Man possesses actual otherwise choice and can, therefore, act or refrain in the moral moment of decision even with the same past within a given range of options. Extensivism contends God endowed man with this ability, which is an aspect of being created in the image of God. God determines the range of options. Adam’s range of options before the fall was greater than humanity’s options after the fall. The range of options available before the fall was the result of creative grace.
Fallen man can still choose between options. He did not lose his libertarian moral freedom, but the range of options is less than man had before the fall. Since the fall, man has lost the ability to make choices that are inherently righteous or spiritually restorative (making one right with God) based solely on creative grace. To make an inherently righteous or spiritually restorative choice, God had to provision redemptive grace, grace enablements.
For compatibilism to be the biblically reflective approach to understanding Scripture (what the Bible actually portrays and teaches), Calvinists would have to explain why the Bible, from Genesis 2 through Revelation 22, is absolutely permeated with verses, events, challenges, commands, offers, and judgments that clearly reflect that people have libertarian free will. That is to say; they can choose to act one way or differently in a myriad of passages (Gen 2:17-3:24; Josh 24; Jer 32; Mark 10:17-31; Rev 22:17-21).
Libertarian freedom allows for both determined events (events uninfluenced by human choice) and undetermined events (events influenced or caused by human choice) in which people choose between options. And whatever they did choose, they could have chosen differently even with the same past.
Compatibilism, Calvinism, requires that everything is determined, and if there is even one verse (I believe there are hundreds if not thousands that do so) that demonstrates the person had the freedom to choose differently than he chose, in the moral moment of decision, Calvinism and compatibilism collapse into an unbiblical perspective.
Consequently, unless a person can demonstrate the Bible teaches only micro-determinism (every verse that speaks of choosing reflects only a predetermined choosing wherein the appearance of having the freedom to choose differently is an illusion), he should totally and quickly disavow Calvinism. If a person chooses to remain a Calvinist, he is integrity bound to speak consistently with the micro-determinism of his position. In my book, Does God Love All or Some? I demonstrate that Calvinism’s view of moral freedom is absolutely in conflict with the teaching of Scripture when we consider all the Scripture.
What makes the micro-determinism in Calvinism, compatibilism, so difficult to detect is that Calvinists often interpret, talk, and teach the Scripture libertarianly. Meaning, they do so as though there is an undetermined choice involved, i.e., man can choose among the options available in the passage, and whatever he does choose, he could have chosen differently. Now, while that is true to the Scripture, it is in absolute contradiction to compatibilism, Calvinism.
Therefore, if a Calvinist is not going to live, speak, teach, interpret Scripture, and pray in a way that is consistent with micro-determinism so that both the Calvinist and the one whom he engages understands his deterministic perspective, he should disavow Calvinism.
 To see a full explanation of what each view entails see chapter seven in Does God Love All or Some: Comparing Biblical Extensivism and Calvinism’s Exclusivism.
 Here I am using Extensivism as a synonym for non-Calvinism. In five point Calvinism, such things as God’s love, offer of salvation, payment for sin, and call to salvation are limited exclusive, whereas, biblically they extend to everyone, and are, therefore, extensive.