  A leading way to constrain physical theories from cosmological observations
is to test their predictions for the angular clustering statistics of matter
tracers, a technique that is set to become ever more central with the next
generation of large imaging surveys. Interpretation of this clustering requires
knowledge of the projection kernel, or the redshift distribution of the
sources, and the typical assumption is an isotropic redshift distribution for
the objects. However, variations in the kernel are expected across the survey
footprint due to photometric variations and residual observational systematic
effects. We develop the formalism for anisotropic projection and present
several limiting cases that elucidate the key aspects. We quantify the impact
of anisotropies in the redshift distribution on a general class of angular
two-point statistics. In particular, we identify a mode-coupling effect that
can add power to auto-correlations, including galaxy clustering and cosmic
shear, and remove it from certain cross-correlations. If the projection
anisotropy is primarily at large scales, the mode-coupling depends upon its
variance as a function of redshift; furthermore, it is often of similar shape
to the signal. In contrast, the cross-correlation of a field whose selection
function is anisotropic with another one featuring no such variations -- such
as CMB lensing -- is immune to these effects. We discuss explicitly several
special cases of the general formalism including galaxy clustering,
galaxy-galaxy lensing, cosmic shear and cross-correlations with CMB lensing,
and publicly release a code to compute the biases.
