There is a slight historical basis for fictional witch and monster hunters.
There were real professional hunters of heretics in the middle ages and early modern era.
Roman Catholic ones often belonged to one of the several inquisitions, such as the Medieval Inquisition (consisting of the Episcopal ((Bishop's)) Inquisition c. 1184-1230s and the Papal Inquisition founded in the 1230s), the Spanish Inqisition (1478-1834), the Portuguese Inquisition (1536-1821), and the Roman Inquisition, established in 1542 and still existing at the present, though it lost its authority to inflict secular punishments like imprisonment or death centuries ago.
In the Middle Ages, many European people believed in folk tales and superstitions about witches who could use magic to do you favors or harm you. So there were many accusations that people were witches using magic to harm. And the Catholic church usually took the position that witches and witchcraft were imaginary and that belief in witchcraft was heresy. So Medieval Inquisitors usually didn't hunt witches very often.
But during the 15th century, the Catholic Church reversed its position on witchcraft 180 degrees. The turning point might have been in the 1480s.
In 1484, Dominican Inquisitor Heinrich Kramer attempted to start witchcraft trials in the Tyrol. But he was accused of illegal methods and expelled from Innsbruck. Kramer obtained from Pope Innocent VIII on 5 december 1584 a papal bull Summis Desiderantes Affectibus giving Kramer authority to persecute heretics and witches in the dioceses of Mainz, Trier, Cologne, Salsburg, and Bremen. And Kramer began writing a book on how to prosecute witches.
The Malleus Maleficarum, usually translated as the Hammer of Witches, is the best known treatise on witchcraft. It was written by the Catholic clergyman Heinrich Kramer (under his Latinized name Henricus Institoris) and first published in the German city of Speyer in 1486. It endorses extermination of witches and for this purpose develops a detailed legal and theological theory. It has been described as the compendium of literature in demonology of the 15th century. The top theologians of the Inquisition at the Faculty of Cologne condemned the book as recommending unethical and illegal procedures, as well as being inconsistent with Catholic doctrines of demonology.
The Malleus elevates sorcery to the criminal status of heresy and recommends that secular courts prosecute it as such. The Malleus suggests torture to effectively obtain confessions and the death penalty as the only certain remedy against the evils of witchcraft. At the time of its publication, heretics were frequently punished to be burned alive at the stake and the Malleus encouraged the same treatment of witches. The book had a strong influence on culture for several centuries.
Jacob Sprenger's name was added as an author beginning in 1519, 33 years after the book's first publication and 24 years after Sprenger's death; but the veracity of this late addition has been questioned by many historians for various reasons.
The Malleus Malificarum claimed that there was a secret cult of devil worshipping witches who used their magic powers to inflict harm on their Chrisitan neighbors. It claimed that the witch cult was a "clear and present danger" to the survival of Christendom and so should be destroyed using the harshest possible measures.
So when people accused other people of being witches in the folklore sense, inquisitors and secular lawmen often interpreted that as accusing them of being witches belonging to the imaginary witch cult of the Malleus Malificarum and used the harshest possible methods to try, convict, and execute those alleged witches.
For one, two, or three centuries in different countries of Europe people were tried for witchcraft, and according to various estimates a total of tens or hundreds of thousands of people were executed.
The general rule in witchcraft trials was that the accused was considered guilty until proven guilty, and it was usually impossible for an accused witch to be acquitted. Katerine Kepler (1546-1622), mother of Johannes Kepler, was one of the very few persons acquitted after being formally charged with witchcraft.
So after about 1500 any Catholic inquisitor whose job was hunting heretics would also have the job of hunting witches. And any lawman in a Catholic country could be called upon to hunt witches at any time.
But the Reformation began just a few decades after Malleus Malificarum was published, and large parts of Europe became no longer Catholic.
An example of a Protestant who was a professional witch hunter for a while is Matthew Hopkins (c. 1620-1647) in the years 1644-1647.
Matthew Hopkins (c. 1620 – 12 August 1647) was an English witch-hunter whose career flourished during the English Civil War. He claimed to hold the office of Witchfinder General, although that title was never bestowed by Parliament. His activities mainly took place in East Anglia.2
Hopkins' witch-finding career began in March 1644 and lasted until his retirement in 1647. He and his associates were responsible for more people being hanged for witchcraft than in the previous 100 years, and were solely responsible for the increase in witch trials during those years. He is believed to have been responsible for the executions of over 100 alleged witches between the years 1644 and 1646.
It has been estimated that all of the English witch trials between the early 15th and late 18th centuries resulted in fewer than 500 executions for witchcraft. Therefore, presuming the number executed as a result of investigations by Hopkins and his colleague John Stearne is at the lower end of the estimates, their efforts accounted for about 20% of the total. In the 14 months of their crusade Hopkins and Stearne sent to the gallows more accused people than all the other witch-hunters in England of the previous 160 years.
So there have been historic witch hunters, although in modern times they are usually depicted as villains instead of heroes.
And as far as I know that is the only factual basis for the fictional depiction of heroic witch and monster hunters.