In Tahmid's blog there is mention / question re the need
for snubbers. The reply focused on the FET stress and
neglected the ringing / EMI concern. Abrupt dI/dt or dV/dt
(and you have both) will kick the tank (Coss of FET, and
some inductance term(s) of the xfmr primary) and nothing
to scrub off that energy.
Another push-pull concern is "flux walk" which comes from
leg-leg circuit imbalances such as on-time, component
mismatches etc. More sophisticated controllers may have
features to sense and correct that, otherwise be sure to
leave yourself plenty of core saturation margin and maybe
a soft saturation characteristic (i.e. no "cliff").