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.)