The guilt is real.
Every human has the same God-given understanding of what is right and wrong.
“Conscience” is actually “conviction”. Sarah Palin, by her example, is convicting a lot of people who want to believe that evil is good.
The reason these people are so vehement, and so upset about it is that they KNOW they can’t get right with God without admitting that what they did was wrong and asking forgiveness. It is such an abhorrent thing that it has to be a huge burden, and then if you’ve compounded it by justification and encouragement of others to do it... I can’t imagine the guilt. It would definitely lead to depression.
You're very close, but I don't think most of those people believe, whether at the intellectual or gut level, that repentance is the path to atonement. Instead they believe, at the gut level, (and possibly the intellectual level as well) that the only path to atonement is to make abortion not be wrong. They insist that abortion be considered "okay" because they believe, in the strongest possible way, that they absolutely, positively, urgently, and critically need for it to be "okay".
Were it not for the fact that some "pro-life" people would almost certainly mess things up, I would suggest that t-shirts saying "I regret my abortion" could trigger a major sea change. In practice, I'd be very worried that people wearing such shirts would get harassed as evil-doers by people who call themselves "pro-life", but if pro-life people would refrain from such harassment (or even excessive unsolicited efforts at consolation), I would think it could start a movement that would totally bury the "pro-choice" camp.
If the "pro-life" people were willing to support the wearers of such shirts when asked to do so, but otherwise refrained from bothering them, I would think many wearers would quickly found that the shirts made them feel better. They would no doubt be attacked by so-called "pro-choice" people, but if they were warned of such attacks beforehand and told that braving such attacks by evil people is a mark of honor, I would think those that stood firm could find themselves freer of guilt than they'd been for years.
And when bright smiling people wearing such shirts are asked by others who have had abortions why they're smiling so much if they're plagued with guilt from their abortion, they could reply that their shirts brought them a freedom they'd been searching for but never found.
Note that there's no need to bring religion into this. Religious teaching can be offered if requested, but keeping the shirts secular would avoid triggering the "anti-religion" reflex of the people who most need redemption.