I've just re read this and it seems there's more to it than we are being told.
"All was fine until we had our baby boy, now 2.5 years old."
So they weren't swearing or cursing or noisy or bothering you before that?
The heresay comment about threatening to kill someone's dog - was that because it was a noisy dog? Obviously NOBODY is saying it is ok to threaten to kill a dog - but owners who don't care about noise from animals make people's lives an utter and total misery.
And we have no idea at all what was actually said, you weren't there for the comment either.
I wonder if one or both of them is just super sensitive to noise. That can and does definitely make people react badly and yes, curse and swear.
No point in saying they can or should control themselves, some people absolutely CANNOT control becoming aggro because of noise, look up misophonia. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9292922/#:~:text=Misophonia%20involves%20a%20decreased%20tolerance,to%20be%20able%20to%20do.
Based only on the information you have given, it sounds like their lives are being made a total misery by other people's noise levels.
Modern noise exposure is linked to poor health outcomes. https://bmcpublichealth.biomedcentral.com/articles/10.1186/s12889-015-1671-z#:~:text=Results,associated%20to%20high%20blood%20pressure.
It's true that noisy children have always been a problem for many though - and true that often not much can be done about it.
But it sounds like your neighbours are reactive, not active in this situation.
And just because a noisy child is normal and he is doing nothing wrong doesn't make it bearable for some.
And now you want to stop them from even swearing about it in their own home - perhaps the only outlet they actually have for their misery.
Perhaps you can't help your son being noisy, it's normal enough in kids of course, but some people absolutely CANNOT help being upset by noise and it's nonsense to pretend otherwise.
Perhaps you're one of those people who finds anything except total approval and agreement bearable. But you won't get that from your neighbours, clearly.
So the solution is that you continue to ignore them and they will continue to ignore you.
Anyway, it's all guesswork. The point is that your neighbours saying words in their own home to let off steam about a situation they clearly find unbearable is NOT, in fact, your neighbours doing anything at all to you.
And yep, maybe look into that soundproofing.