This has to do with the way we set text to be rendered in the browser. You are able to apply a drop shadow to system fonts (which will be rasterized to an image in the browser), but currently web safe fonts with drop shadow aren't supported in Muse because we still support IE8 and IE9 -- which don't support the shadow effect for text. One sort of work around is to use two text frames, one which holds your text and one which has black coloring with opacity less than 100% applied to the text that gets set behind and offset to your text to appear as though it were drop shadow, while keeping your text live. Group them together and moving them shouldn't throw off your design too much.
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