Why would we stop judging?
We should stop judging.
Because nobody has been able to show "free will" is more than just another belief (as in religion) and it is therefor no basis for rational discussion. And if free will does not exist, our concepts of "merit" (on the positive side) or "guilt" (on the negative side) are worthless and should be abolished.
That's why there should be no judging at all.
(Note: No judging does not mean nobody goes to prison for crime. It simply means we must redefine "punishment" as "a neutral sanction" or better: "protection from happening again".)
If somebody explains you the reason why judging does not make any sense and you understand it and apply it to your life, then it wasn't "free will". It was causality - you're doing it because of a "variable" (the explanation) that was part of your "system". Obviously, there is a huge number of other variables participating in your decision, not just one, and you could track them on a micro level (molecular) as well as on an macro level (i.e. your family, friends, wealth, etc.).
Yes, rational thinking dictates exactly this conclusion (the apparent randomness being introduced by our current understanding of quantum physics).
> And while I think that there is no free will [...] in everyday life I just keep pretending I have free will.
Well, Rome wasn't built in one day. Our whole culture was built upon the illusion of "free will" (same goes for other beliefs like magic, gods, etc). It's a good exercise to remind oneself about this when we get all worked up over something or somebody.
If the logic has a flaw, please let me know, I'm interested in being as close to the "truth" as possible.
As discussed, it would mean, for example, that we cannot judge anyone (and at the same time claim to be rational).
To give an example: The death penalty should no longer exist, because it is solely "justified" by judgement along the lines of "person X is evil and therefor doesn't deserve to live". There are no evil people, only people who do what they have to do, given the variables in "their system". That means there should be no "punishment", but emotionally neutral measures to prevent the suffering from happening again (i.e. locking the person up). It's pretty clear to me that a much more humane society will be the result of this understanding. And who wouldn't want that?
Edit: "rational" in the sense of "logical".
No, it doesn't. I mean, the rational actor model is evidently false for lots of other reasons, but its a purely mechanistic model but for the utility function (on whose nature it is completely neutral), so rationality is just as compatible with the non-existence of free will as it is with the existence of free will (in fact, rationality requires either that there be no free will or that it be confined entirely within the utility function.)
If there is no free will and we still judge, we cannot not judge!
All there needed to be was for the handful of initial variables that were set at the "beginning of our universe" to have such values that their interaction over time would lead us to rational thinking and therefor our understanding that there is no "free" will.
Simply put: If I explain to you why free will is an illusion and you stop judging, then it wasn't a "free" will. It was a cause-and-effect situation.
If there is no free will and I stop judging, then yes, obviously we can stop judging.
But if there is no free will and after your explanation I still judge, then no, we cannot.
My explanation would be only 1 variable in your system (out of an infinity of others, if you assume that you can always continue to "zoom in").
Now, if that 1 variable does anything to your decisions or not depends on all the other variables as well, i.e.: You may have gotten a very religious education which may lead you to accept beliefs put forth by other as "the truth", without questioning. Since one major point of religion is "free will", I'm not sure "my explanation" would do anything to your decision making.
On top of that, how would choice make more sense in a random universe?