Refrigerator pickles in plastic?
Advantages of glass:  you can see the product....the container does not pick up any flavor or color from the product...other than that, in this case (refrigerator pickle) there is no reason not to use your plastic.  In fact, the only reason to use glass, that I can think of, is if you we going to can your pickles for extended shelf life. Then, of course, would would need Mason jars or equivalent.  Fermenting, doesn't have much to do with this question either.  I often store homemade sauerkraut and kimchee in plastic quart containers without issue.