OK, it looks like the apparent grid-iness in the output stdev is just a minor interpolation artifact when the applied transformation matrix is just a small perturbation off of an identity transform. That is, the regridding is just a little different than being an identity, and the interpolation used is low order interpolation (the default in 3dAllineate is "just" cubic); then this kind of thing can appear-- note that it is only really noticeable at the level of looking at the standard deviation. You can get around this by applying a higher-order interpolant in 3dAllineate, such as wsinc5, say via adding "-final wsinc5". (Alternatively, if your data were integer-valued, you could use "-final NN".)

--pt