Whether it's a fog line or a bike lane stripe, treat it as a fog lane stripe and ride to the left of it. Where the lane puts you in danger from right turning trucks, take the lane about 100' before the intersection.
I agree with the others, contact your local cyclist advocacy group. If you don't have on, use this lane as the basis to start one. In the mean time, call and write the city traffic engineers. In my town, they'll often talk to you. That will let you see how they are thinking, and you might be able to resolve it with them. They're good folks to have on your side if you can. If you can't, start calling and writing your local government officials.