  Shadow tomography is a scalable technique to characterise the quantum state
of a quantum computer or quantum simulator. The protocol is based on the
transformation of the outcomes of random measurements into the so-called
classical shadows, which can later be transformed into samples of expectation
values of the observables of interest. By construction, classical shadows are
intrinsically sensitive to readout noise. In fact, the complicated structure of
the readout noise due to crosstalk appears to be detrimental to its
scalability. We show that classical shadows accept much more flexible
constructions beyond the standard ones, which can eventually be made more
conformable with readout noise. With this construction, we show that readout
errors in classical shadows can be efficiently mitigated by randomly flipping
the qubit before, and the classical outcome bit after the measurement, referred
to as $X$-twirling. That a single $X$-gate is sufficient for mitigating readout
noise for classical shadows is in contrast to Clifford-twirling, where the
implementation of random Clifford gates is required.
