Sounds like a car accident waiting to happen. I dont see how you can have a green light to go through the interesection while the traffic to your left ALSO has a green light, albeit to turn left, which puts them on a collision course with your lane's flow of traffic. Complain direct to the city about this hazard, maybe someone programmed the lights wrong, cant imagine there are no accidents at this intersection with two lanes of traffic given green lights into each other.

But, if there is some sort of communication miisunderstanding and you are saying that "green/walk" is the pedestrian signal only and the traffic light is still red then:
Cyclists dont heed walk signals for pedestrians when in the lane of traffic as this confuses drivers and could cause a problem.

Wait for the green traffic signal, cross with your flow of traffic and then carefully either filter up, or take the lane and wait, annoying as it may be. Or take an alternate route. Or walk the sidewalk and avoid all the fuss while enjoying a few swigs from the water bottle etc.