"This question is directed to all our Catholic friends. But of course, all are welcomed to reply. Although my evangelical friends may disagree, my understanding of how they take this verse is that they are first taught that we are saved by "receiving Jesus as Savior" (typically in the form of a prayer, but not always) from a preacher or friend, and then with that teaching they look at John 1:12 only as a confirmation to the paradigm that has already been instilled. I speak only for my own experience, & I do not intend this as a universal statement. I personally have never met an evangelical who looked at John 1:12 and did not automatically conclude that this meant "receiving Jesus as savior", based on prior learning. I do not mean this derogatorally. Just what I've seen. I am open to being corrected if this is not the case."
I see this verse as being about receiving Jesus for who he is. For example, God opens the heart of a person to understand that this is Jesus, straight from God, the savior in human form. When God gives someone that understanding, then they are not thinking so much 'who is this man?' or 'should I listen to this man?' or especially they are not rejecting him as not an authority, because he is not one of their religious leaders. A person who receives Jesus has a heart that recognizes Christ for who he is and is devoted to him notwithstanding other "religious" claims that would contradict him. I do not see it as some sort of formalized prayer that any religion says should be prayed to be saved, though a prayer of inviting Jesus into the heart can be good perhaps. It is hard to imagine a case where asking Jesus into one's heart would be bad. Such an act would not be the thing that saves a person though. Rather, God's act of opening ones heart to truly believe and trust him as savior would. A person who receives Jesus is not rejecting him but welcoming him and his words. Jesus has his own spiritual children today and many groups and religions, including supposedly Catholic or Christian ones, may not recognize the ones who are truly in Christ today and may reject the true children of God today just as many religious persons of Jesus' time rejected him. People and religions may have many institutional and other ways of not recognizing just who these, God's real children, are, and thereby not receive Christ. Further, I think a person who truly receives Jesus will realize that they can talk to God for who he is, the true God of the Bible and the creator and savior. Clearly, John 1:12 and it's surrounding verses are involved with the difference between the saved and the unsaved persons, because it says that one kind of person is born from above and recognizes Christ for who he is, receiving him, whilst another kind of person is not born from above and does not recognized who Christ is nor receive him.