Rinsing the sauerkraut absolutely does work - we do it all the time, both with store-bought and homemade sauerkraut.
Every batch of sauerkraut is different, so rinsing & tasting is the only way to ensure that your dishes turn out appropriately salted.
Yes, some of the salt has entered the cabbage itself, but most of it will be in the brine/on the surface.
If rinsing in a colander isn't enough (and if you used twice the recommended amount of salt it's likely not to be), then you can drain the liquid as best you can, then add clean water to cover, and let it soak.
Rinse and repeat until the salt level tastes more acceptable.
Adding more cabbage and letting it ferment some more is also an option, although the twice-fermented parts can end up rather mushy.
cooking.stackexchange.com/users/2569/Marti
Adding the missing cabbage is a viable solution.
You could also just remove some of the brine and replace it with water, until it's salty to your taste.
Finally, you could just rinse some of the brine off of it before eating it.
cooking.stackexchange.com/users/3994/Nick
Unfortunatly, the amount of salt you used will not allow the fermentation process to occur.
It will preserve the cabbage and is perfectly safe to eat, but it will not be fermented, therefor not saurkraut.
I would advise just tossing it and making some more.
After it has fermented it will be tasty, and if you want you can rinse some salt off then but it will affect the taste somewhat but still be tasty.
J W
cooking.stackexchange.com/users/30899/J W
I too made sauerkraut that was too salty, by adding more water and salt when the level of liquid dropped.
Fortunately the too salty part was mostly on top, but the kraut by itself was still too salty.
I drained the liquid from each jar onto a glass measuring cup (or bowl) and rinsed the kraut in a colander with cold water, squeezing the kraut throughout the process.
Once done, I put the kraut back into the jars and added back the fermentation water (has salt) and the result was good kraut.
Just don't add salt if you are cooking sausages or ribs with your kraut and it too will taste good.
Next time, I will just add more water when the liquid level drops down and no additional salt.
cooking.stackexchange.com/users/59167/Laura Harmon
Since I didn't want to wash off the good bugs along with the salt, I solved the too salty by adding some of my kraut to another recipe from which I had omitted the salt.
In this case, I added two teaspoons of kraut to a bowl of made from scratch coleslaw.
It was delicious.
I think you could also add it to unsalted potato salad, but I haven't tried that one yet.
cooking.stackexchange.com/users/53749/ferryboat George
I recently finished my first batch of sauerkraut and tasted it only to find that it's way too salty. In referencing the original recipe, I realized that I used the amount of salt recommended for 5lbs of cabbage but I only had 2.5lbs.  What, if anything, can I do to salvage the sauerkraut? Because of the way it's made, I wasn't sure that just adding the missing cabbage is a viable solution and part of me wonders if the salt is just part of the food now.
Recovering from Over Salted Sauerkraut
cooking.stackexchange.com
<salt><sauerkraut>
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cooking.stackexchange.com/users/84/Jonathan Campbell
You could rinse the sauerkraut to remove some of the salt before eating it, but excessive salt may impede fermentation and rinsing may wash off some of the good bugs along with the salt. Instead, you can add some of the kraut to another recipe without salt added. Try rinsing it and using in recipes that don't have any salt already. It should even out.
You can rinse it before eating or replace some of the brine with water. There is too much salt for fermentation to occur. Try using the salty sauerkraut with recipes that contain no other salt.