I have seen some similar questions, but I don't think my problem is that I have overlapping faces. I have also tried adjusting the lighting level but the problem persists. When cycles render preview does 1 or 2 out of the 32 render cycles then the coffee looks more or less correct but the end result is always grey and white and washed out. I might be able to fix this with an overlay of color in the nodes, but is there any way to avoid the problem in the first place?
UPDATE: I turned the light intensity down and changed to darker base colors for world and sun light sources. I changed the base color of glass and coffee which improved the glass slightly, but the coffee is still ridiculously reflective. I have roughness at .5 and turning it up to 1 does not help.
Final result after applying instructions in checked answer
and after adding a transparent BSDF and decreasing transmission and increasing roughness of glass
I also decreased the light intensity for world and both lights to .4 for world and about 100 watts for each light down from 600