The question of conversion from Judaism to Christianity primarily concerns Jessica for most of the play. Her love for a Christian man will not end in marriage if she remains a Jew. The practice of enforced conversion was widespread in Europe at the time, while some Jews and Muslims did convert voluntarily. The battle for the soul and the choice of the individual heart go hand in hand.
In Shylock's case, he has expressed no interest in abandoning his own faith. Although his daughter treats him unkindly, he shows concern for her welfare as he agrees that she and her husband will inherit together. Because Christian faith was a requisite for many positions, Jews were often faced with this dilemma.
As Shylock is an experienced man, used to his minority status and related discrimination, and knows of his daughter's desires, it probably was no surprise that the trial would end in judgment against him. He may have been anticipating his next step when he spoke of revenge in act 3, scene 1:
If a Jew wrong a Christian, what is his humility? Revenge! If a Christian
wrong a Jew, what should his sufferance be, by
Christian example? Why, revenge! The villainy you
teach me I will execute . . . .
Thus by the time Portia "asks" him to accept the court's imposition (act 4, scene 1), he does not actually say he will convert. He simply states, "I am content" but also "I am not well. Send the deed after me . . . ." Bear in mind that his money will go to Jessica as inheritance. Shylock may well be biding his time. The baptism does not figure in the play's action, so we cannot say for sure what his next step will be.