  Fast X-ray Transients (FXTs) are a new observational class of phenomena with
no clear physical origin. This is at least partially a consequence of limited
multi-wavelength follow up of this class of transients in real time. Here we
present deep optical ($g-$ and $i-$ band) photometry with Keck, and prompt
radio observations with the VLA of FXT 210423 obtained at ${\delta t \approx
14-36}$ days since the X-ray trigger. We use these multi-band observations,
combined with publicly available data sets, to constrain the presence and
physical properties of on-axis and off-axis relativistic jets such as those
that can be launched by neutron-star mergers and tidal disruption events, which
are among the proposed theoretical scenarios of FXTs. Considering a wide range
of possible redshifts $z\le3.5$, circumstellar medium (CSM) density
$n={10^{-6}-10^{-1}\,\rm{cm^{-3}}}$, isotropic-equivalent jet kinetic energy
$E_{k,iso}={10^{48}-10^{55}\,\rm{erg}}$, we find that we can rule out wide jets
with opening angle ${\theta_{j}=15^{\circ}}$ viewed within ${10^{\circ}}$
off-axis. For more collimated jets (${\theta_{j}=3^{\circ}}$) we can only rule
out on-axis (${\theta_{obs}=0^{\circ}}$) orientations. This study highlights
the constraining power of prompt multi-wavelength observations of FXTs
discovered in real time by current (e.g., Einstein Probe) and future
facilities.
