I think it is more accurate to say that Calvinism preserves, or strongly emphasises, certain emphases in the apocalyptic sectarian Judaism preached by Jesus, that other forms of Christianity do not emphasise as strongly, or even share. And, like other forms of Christianity, it mainly ignores other emphases in His preaching, constructing its own, often materially Biblical, solutions instead, as have other Christianities.
Jesus was a late Second Temple Galilean Jew who preached an eschatological Messianic Judaism that subsequently outgrew its Jewish origins & (in its catholic version) became a mostly Gentile salvationist cult, before being established by the Roman State within the boundaries of the Roman Empire.
In some respects, Calvinism harks back to the political arrangements of pre-Exilic Israel & Judah. It justified its repression of (what are commonly regarded as) other forms of Christianity by citing OT precedents. By contrast, when James and John offered to call down fire from Heaven on an unwelcoming Samaritan village, in imitation of Elijah's calling down fire upon the bands of soldiers sent to arrest him, Jesus forbade James and John to do so:
51As the day of His ascension approached, Jesus resolutely set out for Jerusalem.
52He sent messengers on ahead, who went into a village of the Samaritans to make arrangements for Him.
53But the people there refused to welcome Him, because He was heading for Jerusalem.
54When the disciples James and John saw this, they asked, “Lord, do You want us to call down fire from heaven
e to consume them?”
55But Jesus turned and rebuked them.
f 56And He and His disciples went on to another village.
55 f BYZ and TR include
and He said, “You do not know what kind of spirit you are of. 56For the Son of Man did not come to destroy the lives of men, but to save them.”
Luke 9 BSB
Calvinism has not always been successful in avoiding a wrong spirit.
The problem for the OT Israelite/Jewish polity, and also for Apostolic Christianity, Catholicism & for much pre-US Protestantism, is that all 3 religions are totalising movements - as are the different types of Fascism & Communism. As is much of Islam. They are totalising, in that they allow no "space", intellectual, moral, spiritual, aesthetic, ethical, political, spatial, to any other polity or creed than their own. Calvinism has exemplified this tendency. Nowadays, totalising Christianity has fallen from favour - which makes little sense, if any.
Calvinism shares another problem found in other forms of Christianity. It has to live within the world, & to provide structures & other means for its continuation as a stable & lasting visible society. It, like other Christian bodies, believes that the Second Coming will occur - but, like them, it has to function as though it did not. In that respect, it cannot adopt the apocalyptic sectarian eschatological Messianic Judaism of Jesus - or only in part. And because, like other forms of Christianity, it is separated by many lands, centuries, & cultures from that in which Jesus lived, it has to accommodate itself to the lands, times, & cultures of today. Jesus did not live in a post-Enlightenment, largely secular liberal, multicultural, Europeanised, politically democratic, multi-State, constitutional federal presidential republic. Calvinists in the USA, do. With the best will in the world, they cannot avoid being influenced by the culture in which they live. And that culture is made up of a mixture of influences, many of them not at all Christian in any sense.
The religion preached by Jesus, and that preached by Paul, were preached to different types of society. Paul preached largely to mostly urban Gentiles, Jesus to mostly rural Jews. A Jewish Gospel full of OT assumptions & notions can hardly make the very same impression on urban Gentiles as on rural Jews living under foreign - and quite recent - occupation. The change from a Jewish to a Gentile audience can hardly have left the act of preaching unchanged - and the differences between the Pauline letters, and the Gospels & Acts, bear this out. From preaching the Good News of the Kingdom of God, Jesus Crucified, Raised & Glorified becomes the subject-matter of the preaching in Acts & the Letters. The presence in the NT of these different stages of the Christian tradition has left Christians how to relate them. Which, if either, takes priority over the other, and why ? And, since the Christian Bible includes that of the Jews, how are the Jewish & Christian Scriptures, and their parts, to be related ? The Bible itself gives rather little guidance on these questions. Jesus, again, knew nothing of the NT Scriptures. Calvinism does.