How do Christians who adhere to the maxim “in essentials unity; in non-essentials liberty; and in all things charity” determine what is essential? The phrase has been worded in different but equivalent ways. For example, the Wikipedia article titled In necessariis unitas, in dubiis libertas, in omnibus caritas says:

In necessariis unitas, in dubiis libertas, in omnibus caritas (commonly translated as &quot;unity in necessary things; freedom in doubtful things; love in all things&quot; or more literally as &quot;in necessary things unity; in uncertain things liberty; in all things charity&quot;) is a Latin phrase.
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The maxim is widely quoted in defence of theological and religious freedom, even though it raises the essential question of which things are necessary and which are doubtful or unnecessary. Despite those conflicts, the maxim mandates charity among all.

In  other words, Christians are called to be charitable and maintain unity with other Christians despite potential doctrinal differences, as long as a minimal set of fundamental essential beliefs are commonly shared. Therefore, it follows as a corollary that failure to accept one or more of the essential doctrines by one of the parties immediately warrants the rupture of the unity.
Question: How do Christians who adhere to the maxim “in essentials unity; in non-essentials liberty; and in all things charity” determine what is essential?
The maxim “in essentials unity; in non-essentials liberty; and in all things charity” is widely embraced by many Protestant churches (Church of England/Anglican, Methodist, Evangelical Presbyterian, Moravian, etc.). The phrase in its current form is found in Pope John XXIII's encyclical Ad Petri Cathedram of 29 June 1959, where he uses it favorably.  In the United Methodist Church Book of Discipline, the phrase appears in the doctrinal history section: 57 as &quot;In essentials, unity; in non-essentials, liberty; and in all things, charity.&quot; A few lines later, the mandate is emphasized as &quot;the crucial matter in religion is steadfast love for God and neighbor, empowered by the redeeming and sanctifying work of the Holy Spirit.&quot;  (Taken from the Wikipedia article you based your question on.)
That is possibly the short answer to your question.  However, it’s not as simple as that, more is the pity. Before moving on to doctrinal issues, please be aware that failure by one denomination to accept the essential doctrines upheld by Christian churches does not necessarily “warrant the rupture of the unity”.  What it suggests is that some denominations are perceived to be outside of the unity of Christian churches who uphold fundamental Christian doctrines.  Let’s focus on the main part of your question, “how do Christians determine what is essential?”  We need to compare the earliest Christian beliefs with what we have now to establish what is considered “essential”.
The first documented creed on the Christian faith is known as the Apostles’ Creed, written about 150 years after the death of the apostles.  It in, we have the fundamental beliefs of Christianity:
•   God the Father Almighty, Creator
•   Jesus Christ his only Son, our Lord
•   Conceived of the Holy Spirit, born of the virgin Mary
•   Crucified, died, was buried, resurrected and ascended into heaven
•   Sits at the right hand of God the Father Almighty
•   Will return to judge the living and the dead
•   The Holy Spirit, the Church, forgiveness of sins, resurrection of the body and life everlasting
Source: https://www.gotquestions.org/apostles-creed.html
Later, in A.D. 325 comes the Nicene Creed: https://www.gotquestions.org/Nicene-creed.html
Moving on to A.D. 1571 we have the 39 Articles of the Church of England, adopted by Anglicans and Episcopalians.  Below are the main doctrines:
•   Trinity – Three Persons within the Godhead
•   Jesus – the Word or Son of God – from everlasting, begotten, not created
•   The Holy Ghost – proceeding from the Father and the Son
•   Jesus – died, buried, resurrected, ascended into heaven, and will return to judge humanity
•   Sufficiency of Holy Scripture for Salvation
•   Of the Nicene Creed and the Apostles Creed
•   Of sin, free will, justification (by faith alone), predestination, election and the Church
Source: https://www.churchofengland.org/prayer-and-worship/worship-texts-and-resources/book-common-prayer/articles-religion
More recently, we have the basic beliefs of the United Methodist Church which include:
•   The Triune God – one God in three persons, Father, Son and Holy Spirit
•   The Bible – the inspired word of God
•   Sin – all humans are sinners
•   Salvation through Jesus Christ
•   The Grace of Sanctification
•   The Sacraments of Baptism and Holy Communion
•   Free will and Social Justice
Source: https://en.wikipedia.org/wiki/United_Methodist_Church#Doctrine
What Christians have in common is based on the Bible, which all Christians believe is the inspired Word of God.  Essential to Christian doctrine is the holiness of God, our creator, the eternal relationship between Father, Son and Holy Spirit, and an acceptance that we are all sinners who can only be saved because of what God, in Jesus, has done to pay the price of sin.  All Christians believe in the virgin birth, the life, death and resurrection of Jesus and the judgment to come.  Through the death and resurrection of Jesus, those who believe in Him can receive forgiveness and be sanctified by the indwelling of the Holy Spirit.  They are adopted into God’s family and are spiritually “born again” which results in a transformed life, a life that produces the fruit of the Spirit.  Faith in God, in Christ Jesus and the Holy Spirit are foundational to Christianity.
Any denomination that denies the inspiration of Scripture must remain outside the unity of Christianity; likewise, any denomination that denies the sinful condition of humanity, and the need to repent and believe in Christ Jesus as the only way to God.  The last word (written before the end of the first century) belongs to Jude:

I felt I had to write and urge you to contend for the faith that was once for all entrusted to the saints.  For certain men whose condemnation was written about long ago have secretly slipped in among you.  They are godless men, who change the grace of our God into a license for immorality and deny Jesus Christ our only Sovereign and Lord. (Jude verses 3-4; cf. 2 Peter 2:1-3).

Finally, in light of the comment left by Paul Chernoch, I realise that this brief and simple outline is far from complete.  No doubt others will be able to add to it and explain it better.  It is not my purpose to argue doctrine with others, merely to present some of the “essentials” of Christian unity as you have requested.  There is liberty to be experienced with like-minded fellow believers, even though we do not necessarily agree with every point of view.  That’s where we exercise charity, to put into practice the love of God that we have received and experienced.