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Grade crossings are everywhere in the Netherlands, but bikes have the right of way, and drivers and pedestrians don't, and that's also how the justice system judges things.
In most US states afaik, the legal incentives are definitely not there to care about bikers.
The reality is in America drivers are not accustomed to bikes passing them on the right when they are turning right. It certainly wasn't part of anything I learned in driver's training (though that was quite a while ago). I honestly could not tell you who has the right of way in that situation. Might vary by state.
So if you're cycling in America and you don't want to get hit, pay close attention to the cars on your left at crossings. Assume they don't see you. In fact as a general rule, assume the cars don't see you.
That's the main reason I rarely cycle in traffic. Too risky, and right-of-way or not, if a car hits a bike, the bike loses.
In modern Oregon's DMV driver's book they specify this case and tell you that they have the right of way, they also include this question in the test. Not sure how it helps on the roads to cyclers, but at least they teach about it.
Compare it to NYC's efforts here where they've intentionally been adding a lot of stripes into intersections for traffic calming reasons alone to force drivers to pay more attention to their overall surroundings, especially on dangerous left turns.
https://www1.nyc.gov/html/dot/html/pedestrians/left-turn-tra...
It may vary by state, but at least here in Iowa cars are supposed to merge into the bike lane (as far as possible) before turning right, not turn across it. This is the same as any other situation where you have two lanes of traffic going the same direction—you start your right turn from the rightmost lane. Bikes are expected to pass turning cars on the left in the regular traffic lane, not on the right.