I'm a kosher consumer and I eat only kosher meat and poultry. I've brined kosher turkeys for years, and have never had any guest complain that it's too salty.
It's important to understand that koshering a bird or meat is not the same as brining it. The koshering (or kashering) process involves 3 parts (many more, but only 3 that are relevant to this discussion): soaking, salting, and rinsing. First, it's soaked for 30 minutes, then it's salted and the salt remains on the meat or poultry for one hour, and then it's rinsed 3 times.
How long do you brine? I brined my turkey this year for 2 days, served it to 17 guests, and got not one comment about it being salty. And, they all knew that I had brined it, and it was very moist. I smoked it for about 4 1/2 hours.
So, let's please put the idea that koshering is equivalent to brining to bed, because, unless you know the specifics, it may look very similar, but the timing makes them very different. And, remember, the point of koshering is to draw out stuff (the blood), and the point of brining is to introduce moisture, so, if they each do what they're supposed to do, one would want to brine a kosher bird even more than a non-kosher one, because the kosher one has had stuff drawn out, not introduced.
Thx for listening.