anamazingfantasy hit the key point here: the object isn't what the person's opinion is. It's the notion that there's still a chance for them to redeem themselves.
For the first lady, her opinions are reprehensible. I know of one person who disagrees and he's since been banned for homophobic remarks. At the same time, however, you'll notice that the focus isn't on her, per se, but her children. Her children just want their mother back. Her opinions are opinions. They sting, they're disgusting, but it's never stated that she actually abused or kicked them out because they were LGBT.
Here lies the first point of this scip: the need to be in a group. If there's anything I've learned over the years, it's that being alone is the most terrifying feeling in the world. We, as social creatures, are designed to interact. Staying alone is a horrible experience. It's why sitting time out in the corner was a usually decent form of punishment and humiliation, while solitary in prison is just awful.
People are more likely to express their opinions while they have people around them with the same ideology. It's why the Nazis and the KKK are so vocal. They know they have people around them to support them. When you take away this social aspect, people become frustrated and confused. They lash out at loved ones who don't feel the same way, they act defensive - it's all a part of human nature.
The woman, in this scenario, is in her own solitary. Unable to adapt to the changing times, she finds herself arguing with others over who gets to sleep with what gender. She's confused, because she comes from a time where such opinions were the norm, and she's frightened - because she's not used to this. Lashing out, she deepens her own hole, which culminates in her dying alone. The withered plant is to show the death of possible redemption.
People won't change their opinions just because you want them to. People don't like to be wrong. You can't expect someone to act how you want them to act by flat out confronting them. Hell, I wish that was possible so that "truthers" would stop humiliating families. By showing support, you remind people that they're not weird, allowing them to gradually lower their defenses and confide in you. At that point, it's easier convince them to see the issue from your point of view.
An analogy would be throwing a siege versus inviting the enemy commander to drink tea, in front of everyone, and becoming his friend so he warmly invites you into his home the next time you meet up.
Now for the second one: again, I completely agree with you that he's a piece of shit. This section is unique because we notice clashing between the woman's thoughts and her actions: the notes claim her thoughts still love him but there's no action to indicate she'll ever fix it.
Here, we focus not on the person's past, but active attempt to redeem himself. He's penning letters, begging for a second chance. He knows he's done shit, and he wants to redeem himself.
The problem however, is that we notice that this conflict will not resolve. The woman explicitly states that even she has limits to her patience. Here we feel bad for the man, not because he's a shit stain, but because we know how this cycle goes: fits of mania, possible psychosis, possible return to alcoholism - everything he swears not to do, he will do. We pity the man not because he doesn't get an answer but because we know he won't escape his cycle of violence.
The Foundation, if you read it again, never explicitly helped them. They just administered amnestics. Who knows, maybe they were F-class amnestics, and they lived on without remembering either person exists. It also raises another question, "Would an instance still appear if neither person remembers the dispute?"
As anamazingfantasy stated, they're still humans. Considering how often we do give second chances (although the American criminal system is a terrible example), there's no reason that such people can't be given a chance to redeem themselves.
I mean, we have all these heartwarming tales about D-Class, who supposedly did something so horrific that they were forced onto death row, yet they do such heroic tales that they either become immortalized in tales or even be pardoned by the Foundation. If such people can be given a second chance, I don't see why an asshole with a shitty opinion can't be given the chance to reevaluate their life.
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