This should be how it is regardless of whether or not a kid is referred to with binary gender terms, though. Segregating toys by the intended owners’ genitals — which is all that really differentiates the sexes of pre-pubescent children — is a ridiculous practice. The same goes for clothing and just about everything else a child might want or need.
I fully support parents choosing gender-neutral pronouns for their newborn children if they wish, but we can achieve a more gender-expansive world even if people continue to assign sex and presumed gender at birth. We just need to decouple “boy” and “girl” from any expectations or stereotypes of a child’s preferences, personalities, or future career options.