SuttaCentral
The Mangala Sutta states,
Not to associate with the foolish, but to associate with the wise; and to honor those who are worthy of honor — this is the greatest blessing
Are there any suttas where the Buddha encourages compassion to the unwise? Where he specifically welcomes people who have done bad things? Where a real “bad” person has even attained enlightenment? I’m looking for suttas with themes of forgiveness, acceptance, non-judgment.
Thank you!
The first that comes to mind is Angulimala.
The pali word which you are looking for is ‘bāla’. Though, if you search you will also get ‘bala’ which means ‘power/strength’.
This is the bālavagga (chapter on fools) in the AN2s
There is the chapter on fools in the Dhammapāda
The balapaṇḍitasutta (the foolish and the wise) MN129
and if you jump over to the index.readingfaithfully.org There is a whole section on fools 
You want fools, we got fools!
Don’t forget stupidity or unwise.
You might also want to take a look through admonishment.
I think the story of Aṅgulimāla in MN 86 is maybe what I am looking for. But I find it hard to believe. The Buddha just scolds him and this supposed serial killer/warlord just…becomes a monk?
I know there are suttas in the Therigatha of former prostitutes who write very nice poetry about their liberation. But what about their process of getting to that point? How did they even humble themselves enough to be receptive to the Dhamma? How did Buddha even get these really troubled people to listen, and not just laugh him off, ignore him, or worse…
I’m impressed he got people to listen to him, when I would expect most people to ignore him or say his teachings are unrealistic or what have you
In my experience, when you encounter someone who is hostile to you and your beliefs, admonishing them to be a better person, or making some kind of statement about your moral superiority, is usually a bad idea. But this is how the Buddha handled e.g. the murderous warlord in MN 86.
So how do you handle people who might be outright contemptuous or disdainful, scornful or mocking, etc about your Buddhist beliefs? Or, even if they just have zero interest? Is there any reaching out to these folks?
Apparently the Buddha was able to reach out to some quite hostile, sceptical, and troubled people! How should we do the same?
I don’t engage with them if I can avoid it. I usually only tell people about my beliefs if I know them better and know that they are capable of holding a decent discussion. Otherwise it’s just useless.
I also think it’s good to keep in mind that we as normal human beings lack the skills the Buddha had. In that way, there’s no need to think about moral superiority because Buddhist or not - one should look at one’s own faults first. Dhp 50
Your scepticism is justified. The Buddha himself made a point to tell the monks that this was an exceptional person / circumstance and that in in the future we (monastics) should not follow this example. We have rules against giving ordination to hardened criminals.
I’ll disagree here with your characterization of sex workers as “really troubled.”
I mean, doubtless many are troubled, but so too are many bankers and congresspeople and national security advisors and so on. And what could be more humbling than forcing yourself to bed any client that pays?
If anything, I would assume that prostitutes have a deeper knowledge than most of the First Noble Truth.
The Buddha most often advised his followers to avoid fools.
“Mendicants, if others criticize me, the teaching, or the Saṅgha, don’t make yourselves resentful, bitter, and exasperated. You’ll get angry and upset, which would be an obstacle for you alone. If others were to criticize me, the teaching, or the Saṅgha, and you got angry and upset, would you be able to understand whether they spoke well or poorly?”
“No, sir.”
“If others criticize me, the teaching, or the Saṅgha, you should explain that what is untrue is in fact untrue: ‘This is why that’s untrue, this is why that’s false. There’s no such thing in us, it’s not found among us.’
If others praise me, the teaching, or the Saṅgha, don’t make yourselves thrilled, elated, and excited. You’ll get thrilled, elated, and excited, which would be an obstacle for you alone. If others praise me, the teaching, or the Saṅgha, you should acknowledge that what is true is in fact true: ‘This is why that’s true, this is why that’s correct. There is such a thing in us, it is found among us.’
-DN 1:1.5.1
That’s a great point. We should try to follow his example in many (if not most) ways, but trying to emulate him in every way will cause trouble.
There is a sutta in the SN where a young monk tries to frame Ven sariputta for something he didn’t do and then that monk is reprimanded by the Buddha. I wish I could remember the reference. Maybe someone else can pull it up
@Pasanna Perhaps you are thinking of this one?
Sāriputta’s Lion’s Roar
Sīhanādasutta AN 9.11
After the rains season, Sāriputta takes leave of the Buddha. Another monk falsely accuses Sāriputta of hitting him before leaving. The Buddha calls Sāriputta to answer the accusation. Before the Saṅgha, Sāriputta denies it, uttering a powerful statement of spiritual prowess.
How do we best practice loving kindness and compassion with people who are unwise and therefore most in need of the teachings?
AN5.162 Dutiya Āghātapaṭivinaya
As you would a sick person.
Thank you for that sutta!