Hard to say for certain from the picture, but it does indeed appear to be a mayfly larva. Unlike damselfly or dragonfly larva, mayflies are herbivores, and will not cause any issues with the fish or other invertebrates. They are also indicators of very good water quality, which makes me question that I.D. in a goldfish tank. They may be damselflies. Distinguishing between the two is easy in person. If the middle filament of the tail is held in line with the other three, and they appear to be only filaments, then you have mayflies. On the other hand, if the filaments appear feathery or gill-like (which they are), then you have damselflies. Regardless, neither type of larva is likely to get big enough to cause any issues with goldfish, so leaving them to play out should be fine.
Since the picture appears to show gills on the abdomen rather than on the tail filaments, I'm more inclined toward the mayfly larva, even though it is a goldfish tank.