I parented gender neutrally, back in the halcyon days 15 years ago when that just meant I didn't foist stereotypes on my children. Clothes were brightly coloured, baby gear was unisex, toys came from all over the spectrum.
My observation of my teens is that they have their own preferences, but their attitude towards stereotypical behaviour has fluctuated wildly over time. My older boy was a high-energy "snakes, snails and puppy dog's tails" toddler, and at 16 he's still never met a sport he doesn't like but also adores babies. He gets heart-eyes over "tiny humans" and is thinking of studying child development at uni. (He's discounted paediatrics because he'd decided he couldn't deal with it emotionally.)
My daughter was full on pink/sparkles/unicorns at 5, and now at 13 prefers black, shuns anything overtly feminine, and wears combat boots with everything.
My younger boy (11) has always tacked between them - doesn't like stereotypical boy OR girl activities, tends to prefer more "unisex" hobbies (music, Minecraft). He's always the interesting factor for me, because if we'd stopped at 2 I would have seen enough early years gender stereotypical behaviour to have started me questioning my feminism.
My youngest has demonstrated to me that children seem to develop their identities within the family unit and often look for ways to be distinct from siblings as far as their innate personalities will allow. It's like they instinctively go looking for a USP! Gender neutral parenting will give them a wider range of options for being distinct from siblings, both same and opposite sex. They can then choose their USPs based on what suits their personalities.
Gendered parenting, from my observations, can narrow the options considerably. Being one of, say, 4 boys in a family that really pushes very gendered masculinity is going to increase pressure to conform to behaviours that might not actually come naturally, as well as increase competition between siblings.