You might not be able to convince an atheist that abortion is a sin. But plenty of them think abortion is wrong. This idea that you must be religious to be moral is ridiculous.
I was not implying that all those who have no belief in God do not have a moral conscious. However, I am sure the numbers and facts would bear it out that those who do not care about God or believe in God are far more likely to engage in sexually "sinful' practices. YES, I KNOW Christians commit adultery and engage in pre-marital sex, but I am sure their belief in hell, purgatory and the punishment of sin is a major deterrent as well. I know it is for Catholics. So to suggest religion does not formulate one's conscious and actions a profound way would be false in many or most cases, IMO.
You also said:
>>So if the woman repents and goes to confession after her abortion, all is well?<<
"All is well?" Not quite. Are her sins forgiven? Absolutely, unless her confession was not sincere or if she held some known sin back. But there is a very real difference between being "saved" and "being allowed into the kingdom undefiled." If some continually sin, even though they go to confession regularly, I am quite certain they will find themselves in purgatory for a spell before being allowed into heaven. One cannot mock God, so to speak.
I will not take the time to make this case more fully. But I will say this --- David sinned against God by committing adultery with Bathsheba and followed up with greater sins after that. God went His prophet Nathan who convicted David of his sin and caused enormous remorse and sorrow. Davide repented was forgiven, but still he was punished. So sin will still have its consequences if it is of an egregious nature or repeated endlessly.
2 Sam 12:13-18, “David said to Nathan, ‘I have sinned against the Lord.’ And Nathan said to David, ‘The Lord also has put away your sin; you shall not die. Nevertheless, because by this deed you have utterly scorned the Lord, the child that is born to you shall die.’ And the Lord struck the child that Uriah’s wife bore to David, and it became sick…On the seventh day the child died.” Catholic Scriptural Principle #1 – there is punishment for sin even after one has received forgiveness.