I think I'd just do a patterned gray-and-white shower curtain and plan to keep it closed most of the time. I've definitely seen worse!

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Consider installing frosted glass door unit as this will hide a majority of the tile and then choose artwork that you love, either with some of the green in it or not. Maybe paint the grey walls white of some other colour that matches your artwork as this is currently highlighting the dark dingy grey in the tiles. I think doing a white theme and frosted glass and bring in some other colours in the artwork might minimize the green enough to manage for awhile until you redo.

If a plan is in the works to redo then the shower curtain idea is the best