The short answer is yes:
Mark 3:28 Verily I say unto you, All sins shall be forgiven unto the sons of men...
But forgiveness of all sin is conditional:
John 8:24 I said therefore unto you, that ye shall die in your sins: for if ye believe not that I am he, ye shall die in your sins.
Jesus Christ came to save sinners.
Luke 5:32 I came not to call the righteous, but sinners to repentance.
1 Timothy 1:15 This is a faithful saying, and worthy of all acceptation, that Christ Jesus came into the world to save sinners...
God is prepared to forgive the sins of those only who believe the gospel, repent of their evil way of life, are baptised into Christ and live a new life by Christ’s commandments.
Mark 16:16 He that believeth and is baptized shall be saved; but he that believeth not shall be damned (condemned).
Acts 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins...
Romans 6:4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
After baptism sins are forgiven for those who are trying to live by Christ’s commandments if they repent and confess their sin in prayer.
1 John 1:5 This then is the message which we have heard of him, and declare unto you, that God is light, and in him is no darkness at all. 6 If we say that we have fellowship with him, and walk in darkness, we lie, and do not the truth: 7 But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin. 8 If we say that we have no sin, we deceive ourselves, and the truth is not in us. 9 If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
1 John 2:1 My little children, these things write I unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous: 2 And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world.
If, after understanding the gospel, we wilfully continue in sin we will not be forgiven.
Hebrews 10:26 For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins,
God is not mocked. We will reap what we sow.
Galatians 6:7 Be not deceived; God is not mocked: for whatsoever a man soweth, that shall he also reap.
Romans 2:4... despisest thou the riches of his goodness and forbearance and longsuffering; not knowing that the goodness of God leadeth thee to repentance? 5 But after thy hardness and impenitent heart treasurest up unto thyself wrath against the day of wrath and revelation of the righteous judgment of God; 6 Who will render to every man according to his deeds: 7 To them who by patient continuance in well doing seek for glory and honour and immortality, eternal life: 8 But unto them that are contentious, and do not obey the truth, but obey unrighteousness, indignation and wrath, 9 Tribulation and anguish, upon every soul of man that doeth evil, of the Jew first, and also of the Gentile; 10 But glory, honour, and peace, to every man that worketh good, to the Jew first, and also to the Gentile: 11 For there is no respect of persons with God.
Paul describes the two ways of life.
Galatians 5:19 Now the works of the flesh are manifest, which are these; Adultery, fornication, uncleanness, lasciviousness, 20 Idolatry, witchcraft, hatred, variance, emulations, wrath, strife, seditions, heresies, 21 Envyings, murders, drunkenness, revellings, and such like: of the which I tell you before, as I have also told you in time past, that they which do such things shall not inherit the kingdom of God. 22 But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith, 23 Meekness, temperance: against such there is no law. 24 And they that are Christ’s have crucified the flesh with the affections and lusts.
Jesus explains that because the way to life is narrow, not many find it; we have free choice in the matter, for the way is clearly laid out in the Bible; but the majority choose the way of death.
Matthew 7:13 Enter ye in at the strait gate: for wide is the gate, and broad is the way, that leadeth to destruction, and many there be which go in thereat: 14 Because strait is the gate, and narrow is the way, which leadeth unto life, and few there be that find it.
The scriptures were written by inspiration of God to show how we can attain to eternal life in the kingdom of God.
John 20:31 But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name.
To undergo an abortion indicates that we are a long way from understanding the gospel of Jesus Christ.This can be remedied by reading the Bible.
We have to understand and obey the gospel ourselves; the beliefs of others cannot save us.
I hope you have found this helpful.
God bless you,