We sing aloud and rejoice because we have been redeemed (allusion to Zephaniah 3:14). The penalty for our sins has been paid. It was not our doing, not our own effort, but nonetheless the salvation has happened. We were trapped in bondage and there was no way we could earn our way free. Our works were insufficient and by the time we have paid for one sin we’ve accumulated more debt from other sins. The debt we owe is great and increasing faster than we can pay it off. The slavery to sin I s such that we cannot be redeemed by our own efforts and then someone else redeems us. We sing and rejoice. We dance and praise the one who paid the price.
Now here’s the question – do we really recognize that we were not saved by our own efforts? There are some who claim that but in their talk and actions show that they believe it was due to their merit that they were saved. It is the Christianists who require a specific wording or action such as “I have a personal experience with Christ” or “I believe in the inerrancy of Scripture” or have they been slain in the Spirit or do they speak in tongues or …. Putting the burden of a particular turn phrase or a certain doctrine on someone else shows that we do not believe that Jesus – the one who is our Christ – came to save us.
And yes, there are some beliefs that I do not consider Christian. There are some denominations and cults that I believe have strayed from Christianity. Yet the question of who is saved is best left up to God. Talking of particular doctrines as more or less Christian and talking of particular actions as more or less aligned with Christian beliefs is different than pinning salvation on particular actions or beliefs.
Yet what we live by is not statements of belief or actions. We, who are Christian, live by faith in Christ. (Galatians 2:16) And living by faith in a person or a being is very different than living by faith in the law or a doctrine or a set of actions or a set of beliefs. The one you can count whether you’ve been faithful and someone else is faithless. The other is more difficult.
And who is welcome? In God’s realm it is everyone. And we should attempt to do the same.
Zephaniah 3:14-20  Sing aloud, O daughter Zion; shout, O Israel! Rejoice and exult with all your heart, O daughter Jerusalem!  The LORD has taken away the judgments against you, he has turned away your enemies. The king of Israel, the LORD, is in your midst; you shall fear disaster no more.  On that day it shall be said to Jerusalem: Do not fear, O Zion; do not let your hands grow weak.  The LORD, your God, is in your midst, a warrior who gives victory; he will rejoice over you with gladness, he will renew you in his love; he will exult over you with loud singing  as on a day of festival. I will remove disaster from you, so that you will not bear reproach for it.  I will deal with all your oppressors at that time. And I will save the lame and gather the outcast, and I will change their shame into praise and renown in all the earth.  At that time I will bring you home, at the time when I gather you; for I will make you renowned and praised among all the peoples of the earth, when I restore your fortunes before your eyes, says the LORD.
Galatians 2:11-21  But when Cephas came to Antioch, I opposed him to
his face, because he stood self-condemned;  for until certain people came
from James, he used to eat with the Gentiles. But after they came, he drew back
and kept himself separate for fear of the circumcision faction.  And the
other Jews joined him in this hypocrisy, so that even Barnabas was led astray by
their hypocrisy.  But when I saw that they were not acting consistently with
the truth of the gospel, I said to Cephas before them all, "If you, though a
Jew, live like a Gentile and not like a Jew, how can you compel the Gentiles to
live like Jews?"  We ourselves are Jews by birth and not Gentile
sinners;  yet we know that a person is justified not by the works of the law
but through faith in Jesus Christ. And we have come to believe in Christ Jesus,
so that we might be justified by faith in Christ, and not by doing the works of
the law, because no one will be justified by the works of the law.  But if,
in our effort to be justified in Christ,we ourselves have been found to be
sinners, is Christ then a servant of sin? Certainly not!  But if I build up
again the very things that I once tore down, then I demonstrate that I am a
transgressor.  For through the law I died to the law, so that I might live
to God. I have been crucified with Christ;  and it is no longer I who live,
but it is Christ who lives in me. And the life I now live in the flesh I live by
faith in the Son of God, who loved me and gave himself for me.  I do not
nullify the grace of God; for if justification comes through the law, then
Christ died for nothing.