Let us also have a look at the following passage in the New Testament:
Matthew 22:23-33
23 That same day the Sadducees, who say there is no resurrection, came to him with a question.
24 “Teacher,” they said, “Moses told us that if a man dies without having children, his brother must marry the widow and have children for him.
25 Now there were seven brothers among us. The first one married and died, and since he had no children, he left his wife to his brother.
26 The same thing happened to the second and third brother, right on down to the seventh.
27 Finally, the woman died.
28 Now then, at the resurrection, whose wife will she be of the seven, since all of them were married to her?”
29 Jesus replied, “You are in error because you do not know the Scriptures or the power of God.
30 At the resurrection people will neither marry nor be given in marriage; they will be like the angels in heaven.
31 But about the resurrection of the dead—have you not read what God said to you,
32 ‘I am the God of Abraham, the God of Isaac, and the God of Jacob’[a]? He is not the God of the dead but of the living.”
33 When the crowds heard this, they were astonished at his teaching.
The Jews were referring to Deuteronomy 25:5 from the Old Testament where it states that if a woman’s husband dies, and she didn’t have any kids from him, then she must marry his brother regardless whether he had a wife or not.
As we can see from the above passage, when the Jews brought this situation up to Jesus (pbuh) in Matthew 22:24-28, Jesus did NOT prohibit at all for the childless widow to marry her husband’s brother (even if he were married). Instead, Jesus replied to them by saying that we do not marry in heaven, and we will be like angels in heaven (Matthew 22:30).
In other words, if Jesus (pbuh) allowed for a widow to marry her former husband’s brother even if he were married, then this negates the Christians’ claim about the Bible prohibiting polygamy.