How do Antonio and Shylock feel about each other's religions in act 1, scene 3 of The Merchant of Venice?

Antonio, in contrast to his warm and generous feelings toward Bassanio, feels hatred and contempt for Shylock's being a Jew. We learn from his conversation with Shylock that Antonio has a history of speaking in a cruel and derogatory way toward Shylock. He's even spit on Shylock. As Shylock notes:

Signor Antonio, many a time and oft

In the Rialto you have rated me

About my moneys and my usances.

Still have I borne it with a patient shrug,

For sufferance is the badge of all our tribe.

You call me misbeliever, cutthroat dog,

And spet upon my Jewish gaberdine.

I am as like to call thee so again,

To spet on thee again, to spurn thee too.

If thou wilt lend this money, lend it not

As to thy friends, for when did friendship take

A breed for barren metal of his friend?

But lend it rather to thine enemy,

Who, if he break, thou mayst with better face

Exact the penalty.

How like a fawning publican he looks!

I hate him for he is a Christian,

But more for that in low simplicity

He lends out money gratis and brings down

The rate of usance here with us in Venice.

If I can catch him once upon the hip,

I will feed fat the ancient grudge I bear him.

What is the religious root of the conflict between Antonio and Shylock in The Merchant of Venice?

The conflict between Antonio and Shylock arises partly from religion and partly from economic causes. Antonio wants to borrow money from Shylock, who is employed as a moneylender. While he needs Shylock, Antonio also curses him. In addition, Shylock is Jewish, and Antonio is Christian, and anti-semitism on Antonio's part is a reason behind the feud between them. Shylock says to Antonio:

"Signior Antonio, many a time and oft/In the Rialto you have rated me/ About my moneys and my usances:/ Still have I borne it with a patient shrug, /For sufferance is the badge of all our tribe. /You call me misbeliever, cut-throat dog,/ And spit upon my Jewish gaberdine, /And all for use of that which is mine own."

In other words, Antonio has cursed Shylock for being a money lender, as "usances" refers to the practice of lending money and charging interest. Shylock believes he has handled this abuse with patience, as Jews suffer patiently and often at the hands of Christians who mock them. Antonio has abused Shylock and even spat on him because Shylock lends out money that belongs to him. However, Antonio now needs money from Shylock, which causes their conflict to become even more bitter.

Many critics, including the preeminent Shakespeare scholar Harold Bloom, have called the play anti-semitic. In his 1998 book Shakespeare and the Invention of the Human, Bloom charged that the play resulted in many centuries of anti-semitism in Europe, ending in the Holocaust. See the link to the Smithsonian article below for more information about the problematic nature of the play and the debate about whether it is anti-semitic in nature. There is no doubt that religion is at the core of the conflict between Antonio and Shylock. 

How does the relationship between Shylock and Antonio affect the plot?

Short answer: The relationship between the Venetian moneylender Antonio and the Jewish usurer Shylock is one of animosity and mistrust. With such conditions in their relationship, Shylock's loaning of money to Antonio takes on extraordinary conditions that affect other characters as well, such as Portia, who comes to Antonio's defense in the end.

The history of Venice is one of many conquests and advancements, as well as conflicts with those who were not Venetian. Among those held in disdain were the Jewish merchants who had come to this wealthy city of commerce. Before the time of Shakespeare's writing The Merchant of Venice, Jews were confined to the Ghetto Nuova, a small, dirty island, and there were only certain hours that that they were allowed out. In addition, there were other restrictions placed upon them, such as having to wear a yellow hat or a yellow badge. Later, at the time of Shakespeare's play, Jews were allowed in Venice, but confined to a ghetto designated for them.

Antonio is a typical Venetian moneylender who has disdain for the Jew Shylock because of his usury; that is, because he charges exorbitant rates of interest on the money that he lends.

I hate him for he is a Christian;
But more for that in low simplicity
He lends out money gratis, and brings down
The rate of usance here with us in Venice. (1.3)

This disdain that Antonio possesses sets the tone for the plot of Shylock's strangely conditional lending money to Antonio

Signior Antonio, many a time and oft
In the Rialto you have rated me
About my moneys and my usances;
Still have I borne it with a patient shrug,
For suff'rance is the badge of all our tribe (2.7)

Likewise, it also opens the way for the subplot of Launcelot's departure from the service of Shylock, Jessica's renouncing her faith and leaving home to be with Lorenzo, a Christian. And, most of all, it opens the way for Antonio, in the main subplot, to have enough money to help his friend Bassanio, who wants to marry Portia, along with driving this subplot to its conclusion as Portia saves Antonio from losing a pound of flesh. Certainly the antipathy between Antonio and Shylock helps to develop the dimensions of friendship, brotherly love, and male/female love.

How does Antonio and Shylock's relationship affect The Merchant of Venice's plot?

Before the play even starts, Antonio and Shylock have a very antagonistic relationship. It drives the play’s most suspenseful plot elements. Antonio disapproves of Shylock’s financial practices and lends money free of interest, competing with Shylock’s moneylending. Shylock reports that Antonio publicly condemns his usury and hates him for being Jewish:

You call me misbeliever, cut-throat dog,
And spit upon my Jewish gaberdine...
And foot me as you spurn a stranger cur.

Antonio asks to borrow money from Shylock in order to lend it to Bassanio. Because Antonio is opposed to charging or paying interest, Shylock instead imposes a penalty if Antonio does not repay the sum within three months: he wants “an equal pound / Of your [Antonio’s] fair flesh, to be cut off and taken / In what part of your body pleaseth me.”

Shylock assures Bassanio he is joking, and Antonio is sure that he will be able to return the money on time. Unfortunately, both Antonio and Shylock have bad luck, and Shylock demands the pound of flesh. Shylock’s animosity towards Antonio makes it impossible to persuade him. Portia saves Antonio on a technicality, and the only one who suffers in the end is Shylock.

This relationship contributes much to the play. The bond enables Bassanio to woo Portia and then forces Portia to save Antonio for Bassanio’s sake. It creates tension as the audience worries for Antonio’s well-being and sympathizes with Shylock’s anger. It also drives a potential wedge between Bassanio and Portia so early in their romance.

What are the consequences of the rivalry between Antonio and Shylock?

Act I, scene iii offers background on the problems between Antonio and Shylock.

Antonio hates Shylock because he is a Jew and moneylender, and sometimes says and does nasty things to him. Antonio will call him a:

misbeliever, cut-throat, dog / And spit upon Jewish gaberdine

In this period, the Roman Catholic Church banned charging interest on loans believing that doing so took unfair advantage of people in need. Judaism, however, did not prohibit charging interest, and since Jews were subjected to discrimination and persecution, which made it impossible for them to pursue many of the higher-status professions, they would often become moneylenders.

While  Antonio verbally attacks Shylock for lending money, Shylock, not surprisingly, hates Antonio for insulting and shaming him. He also hates it when Christians lend money without charging interest, as this threatens his own business.

Unfortunately for Antonio, he ends up needing a loan for his friend, and has already bitten the hand that will feed him (Shylock's). Shylock wants revenge. In consequence, he offers Antonio an interest free loan but demands that if Antonio can't repay the loan, he forfeit a pound of his flesh, to be cut off any part of Antonio's body that Shylock chooses. Antonio agrees, and then his ships sink so that he can't sell the cargo and repay the loan. Shylock demands his pound of flesh. Since he can demand that Antonio's heart be cut out to repay the loan, this becomes a death sentence. At this point, the play reaches a crisis point.