Silty bottom (precipitate) in ginger ale
That silty precipitate is just a thing that happens when fermenting - it's the yeasts dying off and settling out of the solution.  I've seen it with mead, yeast-based soda recipes, and other fermented drinks (like fermented lemonade etc) - your ginger ale would be yeast based soda, by the way, if you drink while fairly young and carbonated, like with a day or two of fermentation (you can have longer storage if not actively fermenting, ie in the fridge where yeasts are nearly dormant or having killed the yeasties off somehow)  while it will likely grow increasingly alcoholic if you leave it an extended amount of time.

This precipitate isn't a problem, it might be off-putting to see or taste (if you get a whole mouthful) but it isn't harmful and I at least will often drink it because I don't care enough to avoid it, but if you don't like it you can rack the beverage - that is, let it sit still to settle, and gently pour or siphon from the (clearer) top, and stop pouring when just the settled, cloudy yeasty dregs are left.  If you're fermenting for an extended period of time (ie, alcohol) these may be racked several times while aging to keep the yeast from building up and possibly introducing off flavors - though its usually a few months between racking, so I wouldn't expect off flavors to develop quickly.