  A cosmological scenario in which the onset of neutrino free streaming in the
early Universe is delayed until close to the epoch of matter-radiation equality
has been shown to provide a good fit to some cosmic microwave background (CMB)
data, while being somewhat disfavored by Planck CMB polarization data. To
clarify this situation, we investigate in this paper CMB-independent
constraints on this scenario from the Full Shape of the galaxy power spectrum.
Although this scenario predicts significant changes to the linear matter power
spectrum, we find that it can provide a good fit to the galaxy power spectrum
data. Interestingly, we show that the data display a modest preference for a
delayed onset of neutrino free streaming over the standard model of cosmology,
which is driven by the galaxy power spectrum data on mildly non-linear scales.
This conclusion is supported by both profile likelihood and Bayesian
exploration analyses, showing robustness of the results. Compared to the
standard cosmological paradigm, this scenario predicts a significant
suppression of structure on subgalactic scales. While our analysis relies on
the simplest cosmological representation of neutrino self-interactions, we
argue that this persistent - and somehow consistent - picture in which neutrino
free streaming is delayed motivates the exploration of particle models capable
of reconciling all CMB, large-scale structure, and laboratory data.
