1/ "Jesus was talking about forgiveness. When a man (or woman) seeks forgiveness from for their sins, Jesus will forgive each and every time. Those who "cast the stones" were judging based on Old Testament beliefs. However, Jesus was sent to wash away the old and bring in the new. This meant that the judgements and punishments and "rituals" performed in the Old Testament, were no longer necessary. Christ died and rose three days later to take all that away, so that now all we need to do is accept him and follow.
God wants us to love others, not their sin. We are to condemn their sin, as well as acknowledge our own. Hating the act of sin is not the same as hating the individual lost within that sin. I can hate homosexuality and all other sexual sins, but still love the sinner. I don't judge the sinner, God does. All I can do is acknowledge the sin.
"It is not for Christians to pass judgement on them for their souls. Nor is it for them to make them societal outcasts. Jesus would never do such a thing."
Exactly, which is why I mentioned that in the previous paragraph. Condemning the sin isn't judging it. We, as Christians, are to point out the sin and pray for them and God will do the rest. Sinners either reject Christ or they acknowledge their sin and seek forgiveness."
This whole passage is bullshit. For a number of reasons... It isn't about forgiveness, he's talking about hypocrisy. All sin is the same in God's eyes. If you lust, you have sinned, if you murder, you sin. So, if you are not without sin, by all means, you have the means to condemn her. Otherwise you shouldn't.
Even Jesus said this as the pharises brought this woman before him. Jesus, after they left, said "Where are they? Who condemns you?"
"No one." she replied. And Jesus himself said "Then neither shall I."
Be more like Jesus, stop condemning people. Because they're involved in sin that's different than yours.