God Universally Enlightens Man

The Bible is written in such a way that if any man wants to diminish God's work of salvation, the tools are there to reinforce such a perverted teaching. However, in order to completely understand the verse, read the verse with the first and last phrase joined together—they received Him who believed in Him and to them were given the power to become the sons of God.

Notice that the power to become a son of God is given to those who believe and receive; no one is given the power so that they can believe and receive which is what Calvinism teaches.
This truth, along with the teaching of universal enlightenment in John 1:9 "That was the true Light, which lighteth every man that cometh into the world" is another solid refutation of Calvinism. Universal enlightenment simply means that God sends His Light to all. Other passages teach the same thing. Christ draws all men to Him (John 12:32) and thereby enables them to trust in Him (John 6:44). But He only enables those who believe and receive to become the sons of God. This is how He can be the Saviour of all men, but "specially of those that believe" (1Timothy 4:10).

John 6:44 No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.

John 12:32 And I, if I be lifted up from the earth, will draw all men unto me.

1 Timothy 4:10 For therefore we both labour and suffer reproach, because we trust in the living God, who is the Saviour of all men, specially of those that believe. (specially means particularly or chiefly)
Universal enlightenment is NOT universal salvation, but it does signify why there is universal responsibility so that all are without excuse.