If a rail line runs down the middle of the street, does the driver of the train need to obey street signs? For example, if I'm driving a freight train down this stretch of Whitman Street, do I need to stop at the intersection and wait for cross traffic to clear before proceeding?
Authority to put up stop signs comes in part from RCW 47.36.110, and RCW 46.61.190 says that "every driver of a vehicle approaching a stop sign shall stop at a clearly marked stop line...". The definitions for that title (RCW 46.04.670) states that ""Vehicle" does not include power wheelchairs or devices other than bicycles moved by human or animal power or used exclusively upon stationary rails or tracks", so a train is not a vehicle. The operation of trains is governed, on the other hand, by Title 480, and Part 2 of that title includes safety laws. There is a complex federal and state system pertaining to signal systems. Since a train is not a vehicle, it is not subject to the laws requiring vehicles to stop, but it would be suject to any laws requiring trains to stop. Technically, the question could also be whether it's legal for vehicles to drive on train tracks, since I believe the railroad right-of-way was there first, but you could check historical records.
If you drive a freight train and don't have the training to know what you should do, but instead have to ask for the answer on law.stackexchange.com, then you should be fired immediately. You are a danger to the public.
If you are in a car and watch a freight train coming, then given the choice of insisting on your right of way on one side, and not being crushed by a train on the other side, you are free to decide either way, I would opt for "not being crushed by a train".
Usually trains will have signalling lights that tell them whether they can drive or not, broken signal means they need to stop.