With an exception or two, major league rosters are put together so that all of the position players play at least as the short side of a platoon. @Riverbrian has pointed out repeatedly that this is certainly how the Twins are composed. Farmer and Margot are not minimum wage guys--they will play and right now neither (but especially Farmer) are contributing much. It wouldn't surprise me is Julien and Kepler are in the starting lineup tomorrow (Sunday) against a lefty, but it would surprise me if neither Margot and Farmer are not in the lineup.
Maybe what we should be looking for is pinch hitting for the younger left handed players. When a left handed reliever comes in for the Angels today (Saturday) or for the White Sox next week, will there be pinch hitters for Julien, Larnach, Kirilloff and Kepler? That is where I hope progress is made in the immediate future. If any of these guys succeed against lefty relievers, I think their chances for getting more starts against left handers in the future are enhanced. So far, Julien has done very well, but the sample size is still really small.