How would you summarize John Donne's "Satire 3"?

Donne's "Satire 3" is a characteristically learned and witty meditation on the subject of religion. Religious matters were hugely important in Donne's day, and the question of which religion to follow was considered essential both to one's earthly wellbeing as well as to the ultimate destiny of the soul.
The question was of especial relevance to Donne as he changed his own religion from the Catholicism of his birth to Anglicanism, where he rose through the ranks of ecclesiastical preferment, eventually becoming dean of St. Paul's Cathedral.
The poem begins in anguish; Donne doesn't know whether to laugh or cry as his soul is wracked with sin, tormented by the prospect of eternal damnation. Complaining about it will do no good at all. The only cure for sin is a devotion to the religious life:

Is not our mistress, fair Religion, 
As worthy of all our souls' devotion 
As virtue was in the first blinded age?

By "the blinded age" Donne is referring to pagan antiquity. Although that period of history produced many wise and learned men, they were born long before Christ and so were blind to God's word. Instead of Christ, it was virtue, or moral excellence, to which pagans devoted themselves.
 
According to the poem, to avoid the terrible fate of spiritual damnation it is necessary to seek the true religion. Paganism has clearly just been ruled out, but what of the alternatives? Donne personifies various religious options before briefly exploring them. Mirreus represents the Roman Catholic Church that Donne had left. But Catholicism is no good to him. It makes a show of its colorful vestments and opulent liturgy, but in truth the Church is clothed in rags.
 
Then what of Calvinism, represented by the figure Crantz? That's no good either. Calvinism is an exclusionary faith open only to the elect. Worse still, the speaker thinks it can be described in much the same way as a certain kind of woman, one not pleasing to the eye of a man about town such as Donne:


Crantz to such brave loves will not be enthrall'd, 
But loves her only, who at Geneva is call'd 
Religion, plain, simple, sullen, young, 
Contemptuous, yet unhandsome; as among 
Lecherous humours, there is one that judges 
No wenches wholesome, but coarse country drudges



If Catholicism is too outwardly elaborate but spiritually empty, Calvinism has the opposite defects.
 
Phrygius is an agnostic. He believes that all religions are equally bad. Graccus has the opposite problem; he believes that they're all equally good. Phrygius is blind for want of light; Graccus, however, is blinded by too much light. So neither of these approaches will be much help to Donne's audience in its spiritual quest.
 
So that just leaves us with Graius, a personification of the Church of England. Donne's embrace of the Anglican faith doesn't exactly come across as being overly enthusiastic; he seems to have arrived at his faith largely by a process of elimination. Donne's embrace of the state Church appears somewhat lukewarm, to put it mildly:


Graius stays still at home here, and because 
Some preachers, vile ambitious bawds, and laws, 
Still new like fashions, bid him think that she 
Which dwells with us is only perfect, he 
Embraceth her whom his godfathers will 
Tender to him, being tender, as wards still 
Take such wives as their guardians offer, or 
Pay values.



Graius is in the position of the ward who unthinkingly follows the guidance of his guardian concerning marriage. And Donne acknowledges the rightness of this approach even though he is acutely aware that "some preachers" are corrupt, selling their Church like pimps ("bawds") sell women. Still, Donne accepts their word.
 
Although it is essential that we find the true religion, Donne also emphasizes the importance of following one's own conscience. The journey will be long and hard, with many steep climbs and twists and turns:


On a huge hill, 
Cragged and steep, Truth stands, and he that will 
Reach her, about must and about must go, 
And what the hill's suddenness resists, win so. 
Yet strive so that before age, death's twilight, 
Thy soul rest, for none can work in that night.



Whatever destination you arrive at in your faith journey, it is important to be sincere and to go wherever your convictions take you. Donne has made his stand and so must we all while there is still light.
https://www.poetryfoundation.org/poems/44125/satire-iii