Short answers, pulled from the story.
The Polish Brethren were members of the Minor Reformed Church of Poland, a nontrinitarian Protestant church that existed in Poland from 1565 to 1658. They rejected the doctrines of the Trinity and Hell, refused military service, and advocated the separation of church and state. Outsiders called them Arians or Socinians; after their expulsion from Poland they adopted the name Unitarians.
The Polish Sejm expelled the Socinians on the 20th of July, 1658, following a series of seventeenth-century wars known as the Deluge, in which Protestant Sweden invaded Poland. The Brethren, like most non-Catholic Christians, were widely regarded as collaborators with the Swedish enemy.
The church traces its origin to the 22nd of January 1556, when Piotr of Goniądz spoke out against the Trinity at the Reformed synod held in the village of Secemin. The Ecclesia Minor formally organised its own synod in Brzeziny on the 10th of June, 1565, after a debate called by King Sigismund II Augustus failed to reunite the Protestant factions.
The Racovian Academy, formally the Gymnasium Bonarum Artium, was a university founded in 1602 in the town of Raków and closed in 1638. It trained over a thousand students and was the main intellectual and printing centre of the Minor Church. Isaac Newton later collected many books from the Academy.
Fausto Sozzini arrived in Poland in 1579 and applied for admission to the Ecclesia Minor but was refused because of his personal objection to water baptism. He remained among the Brethren as an ally and debater, and his marriage in 1586 to the daughter of Krzysztof Morsztyn Sr. cemented his place in the community. The church's widespread name "Socinianism" came from his grandson Andrzej Wiszowaty Sr.'s publication of his writings in Amsterdam roughly a century later.
John Locke was preceded on tolerance by Samuel Przypkowski and on rational religion by Andrzej Wiszowaty, both Polish Brethren writers whose works circulated in the Netherlands after the expulsion. Isaac Newton met Samuel Crell of the Spinowski family, collected books from the Racovian Academy, and was described as well informed about developments in Poland. The Englishman John Biddle translated works by Przypkowski and the Racovian Catechism, maintaining close ties with the Crellius family.