When Romeo first sees Juliet at the Capulet's feast in act 1, scene 5, his first words about her carry religious connotations.

ROMEO. O, she doth teach the torches to burn bright!
It seems she hangs upon the cheek of night
Like a rich jewel in an Ethiop's ear—
Beauty too rich for use, for earth too dear!
So shows a snowy dove trooping with crows
As yonder lady o'er her fellows shows.
The measure done, I'll watch her place of stand
And, touching hers, make blessed my rude hand.
Did my heart love till now? Forswear it, sight!
For I ne'er saw true beauty till this night. (1.5.46-55, emphasis mine)

Even Tybalt unknowingly takes up the religious theme.

TYBALT. This, by his voice, should be a Montague.
... Now, by the stock and honour of my kin,
To strike him dead I hold it not a sin. (1.5.56-61, emphasis mine)

The scene between Romeo and Juliet that follows is remarkably brief, just 18 lines, and composed almost entirely of religious inferences, references, and metaphors. Juliet doesn't hesitate for even an instant before she joins Romeo in his religious thought and expression.

In the "balcony scene," act 2, scene 2, Romeo picks up where he left off, barely tempering his religious fervor towards Juliet.

ROMEO. She speaks.
O, speak again, bright angel! for thou art
As glorious to this night, being o'er my head,
As is a winged messenger of heaven ...

Call me but love, and I'll be new baptiz'd... (2.2.27-30, 53, emphasis mine)

Juliet abandons further religious allusions, except to refer to Romeo somewhat blasphemously as "the god of [her] idolatry." (2.2.119)

Shakespeare seems intent on showing that Romeo and Juliet's love stands above and beyond mere worldly, secular love. He equates their love with fervent, unwavering, spiritual, even religious love.

Shakespeare also clearly differentiates Romeo's love for Juliet (even if it's love at first sight) from the superficial, lovesick infatuation and purely sexual attraction that Romeo has for the beautiful and unattainable Rosaline.

The religious imagery of Romeo and Juliet's love also serves to lessen the significant negative impact that their suicides—a sin punishable by eternal damnation—would have had on Shakespeare's predominantly Christian audience.

Shakespeare implies that Romeo and Juliet's love is so pure, virtuous, and uncorrupted that they—true martyrs to love—can escape God's judgment for taking their own lives and be "new baptiz'ed," as Romeo foreshadowed in the "balcony scene."

It is difficult to know exactly what an author intended when he made certain choices, especially when we cannot ask him; however, we can discuss possible interpretations and effects of these choices in order to make educated guesses about his intent.

Shakespeare might use religious metaphors and language to characterize Romeo and Juliet's love as actual love, as opposed to simply lust. Romeo is certainly struck by Juliet's beauty at first, and, because of their ages, an audience might be inclined to conclude that what they feel for each other is not real love but simply physical attraction. By referring to himself as though he were a devotee or religious pilgrim, Romeo's metaphors elevate his feelings above the merely carnal; he literally compares them to worship, of a kind.

In addition, the religious meanings and connotations of various words makes the young couple's feelings seem pure and, in some ways, rather innocent, especially in comparison to their parents' feelings of hatred toward one another. While the parents cannot even be civil, and while the adults in the families often act irrationally and cruelly, their children are capable of love, admiration, and something that almost seems to approach the holy. These metaphors make Romeo and Juliet seem more mature; their feelings are more advanced than those of the grown-ups!

In Act I, scene 5 of Romeo and Juliet, the lovers first meet use an extended metaphor to compare Romeo to a pilgrim who is approaching Juliet's sacred shrine. In line 105, Romeo even says that he is acting out a prayer when he kisses Juliet, and he says that "Now my sin has been taken from my lips by yours" (line 106). To reverse that breach of a holy shrine and return his sin to him, Juliet kisses Romeo again.

In one way, this scene can be read as Romeo and Juliet blaspheming religion. They are pretending to be saintly while engaging in forbidden love that their families don't know about. Part of why they use religious language might be to cover up their sins with a religious overlay. In other words, they know they are doing wrong, but are covering it up by pretending to be religious.

In a deeper way, however, Shakespeare is conveying that Romeo and Juliet's love is pure. While their relationship bucks the societal conventions of their day, they love each other, so their love could be seen as blessed by God in a meaningful way.

The formality of the sonnet form and of the religious metaphors connotes the sanctity and sense of purpose in Romeo's approach toward Juliet after he first sees her. The extended metaphor in the fourteen lines, of which each character speaks seven, is that of Romeo being a pilgrim and Juliet a saint. With the setting of the play in the fourteenth century, the time period in which the Canterbury Tales was written, pilgrimages to holy sites were well known travelers, so the metaphors are, indeed, relevant to their lives and timely.

Romeo is in such awe of Juliet's beauty and of the fact that she is unapproachable as a Capulet that he perceives her as one to whom he must not "profane [her] unworthiest hand" (1.5.94); he perceives her as one would a saint. Moreover, he is so touched by her beauty and his charged emotions that he feels moved spiritually as well as physically: 

O, then, dear saint, let lips do what hands do.

They pray; grant thou, lest faith turn to despair. (1.5.102-103)

Romeo and Juliet is a story of young love.  Shakespeare uses religious imagery to reinforce the purity of their love and how they are drawn together like religious pilgrims to a holy site.  He also wrote their conversation as a shared sonnet, which means that as Romeo speaks some lines, Juliet speaks echoing line.

Romeo refers to Juliet’s hand as a “holy shrine” and comments that he is to “profane” it; his lips are “two blushing pilgrims” drawn to her kiss.  Juliet picks up on his religious imagery and makes witty jokes.  As long as he has “mannerly devotion,” she is a saint that he, her pilgrim, may touch.

This conversation is composed as a shared sonnet, and sonnets are love poems; so the religious metaphor leads to perceiving their wordplay as the beginnings of pure love.

Then move not while my prayer's effect I take. 
Thus from my lips, by thine my sin is purg'd. (Act 1, Scene 5)

This is also a witty play on words through which they are forgiven for transgressing with a kiss given in secret.  Shakespeare wants to remind the audience that Romeo and Juliet are innocent youths who are experiencing a newborn, pure love.