AcXx would make quite sense, don't you think?
This fold would be so player dependent, so it is very difficult to analyze in a vacuum.
I think I see myself more often calling than folding.

Calling there seems fine considering the price to call and the fact that you're at the top of your range - additionally villain's line looks incredibly spastic to me.

NO!

Losing with third nutflush happens so rarely like 1 in 50,000 hands that folding here is ridiculous. You won't know enough about the player over a sample size of 90 hands to make an x-ray read. And yeah you might lose, but that's poker, we use statistics not calculus.

Obviously call in theory, but if you think it's a fold just fold imo.

In spots like these I'd suggest just filtering your database for river x/r and going through them.

I raise flop fwiw.

You have to bet bigger on turn and river. You now might get yourself in a spot your range looks capped to 1 or 2 pair.

Why doesn't anybody mention calling in the BB with J4cc when a 20/10 raises the SB? Is there ever a time where a 3-bet / fold isn't better in this situation?

Explain why

Why is it more profitable than folding, if, in the best case scenario we can get (besides having 4 jacks), we are in doubt what we should do when we hit it?

J4s SB vs BB is a standard/easy call. Even if SB is opening 40% we still have like 40% equity vs that Range.

I would bet much larger on the turn. Something like $2.25 maybe even $2.50. along with the River i would bet larger as well. With this Shove i would be calling. our hand is too strong to fold, and if we fold to this line every single time, then our opponent can bluff us very easily because your telling him your only calling with Kx+ Flush and Boats. Its also very hard to flop a flush, and very easy for villain to bluff his 2 pair combos on the river.

How do we know he is opening 40% of hands, if his PFR is around 10%

It's 90 hands, so it might become a bit more around the 20/15 ?

Still, I am still not sure why calling is good here even if we have 40% equity. Don't see a fat margin from calling if we get in doubtful situations where we might either spew or fold to tightly.

Hero does not seem to be knowing what to do with this type of hand post flop in this situation, so why is a call better than a 3-bet in this situation?

That's also true. Good point.

there are weaker hands then a flush thay he could be value betting, plus, you dont exactly reprensent a lot of strenght, although i agree with you that ch raise allin river are not bluff at this limit, well unless you play against me and im on tilit :)