If so how does one know that it's God calling them if they're a part of another religion, or if they are atheists? How do they decline the 'invite'?
Too often people hear a phrase and make assumptions without intending to do so. People talk about God's calling and forget to ask: How does God call people?
"No one can come to Me unless the Father who sent Me draws him; and I will raise him up at the last day. It is written in the prophets, 'And they shall all be taught by God.' Therefore everyone who has heard and learned from the Father comes to Me" (John 6:44-45).
"How then shall they call on Him in whom they have not believed? And how shall they believe in Him of whom they have not heard? And how shall they hear without a preacher? And how shall they preach unless they are sent? As it is written: "How beautiful are the feet of those who preach the gospel of peace, Who bring glad tidings of good things!" But they have not all obeyed the gospel. For Isaiah says, "Lord, who has believed our report?" So then faith comes by hearing, and hearing by the word of God" (Romans 10:14-17).
"As you know how we exhorted, and comforted, and charged every one of you, as a father does his own children, that you would walk worthy of God who calls you into His own kingdom and glory. For this reason we also thank God without ceasing, because when you received the word of God which you heard from us, you welcomed it not as the word of men, but as it is in truth, the word of God, which also effectively works in you who believe" (I Thessalonians 2:11-13).
God calls people to Himself through the message of the Gospel. "For since, in the wisdom of God, the world through wisdom did not know God, it pleased God through the foolishness of the message preached to save those who believe" (I Corinthians 1:21). The calling goes out to all people equally. Whether they heed that call depends on their attitude toward that message, whether they believe it or reject it.