  Gravity theories beyond General Relativity typically predict dipolar
gravitational emission by compact-star binaries. This emission is sourced by
"sensitivity" parameters depending on the stellar compactness. We introduce a
general formalism to calculate these parameters, and show that in
shift-symmetric Horndeski theories stellar sensitivities and dipolar radiation
vanish, provided that the binary's dynamics is perturbative (i.e. the
post-Newtonian formalism is applicable) and cosmological-expansion effects can
be neglected. This allows reproducing the binary-pulsar observed orbital decay.
