Dear Aunt Debbie,
Every Day sounds like an awesome YA version of Quantum Leap. I'll have to check it out.
Your comment about thinking of the narrator of Every Day as male because he/she falls in love with a straight girl, though it sounds like the book is aiming for no assignment of gender, made me think of two things:
The Left Hand of Darkness is an interesting exploration of how deeply gender assumptions and biases are ingrained in human perception. It follows a human ambassador, Genly Ai, who is sent on a peacekeeping mission to a planet on which there is no gender. Every person on the planet Gethen is both male and female, with the ability to shift between genders at will. Because of this, there is no gender bias -- who would you be biased towards, who against? Genly tries to work within this new frame of understanding, but keeps making assumptions about his hosts based on the gender they are currently presenting, and is thrown for a loop when they change. An interesting LeGuin note: in an essay written a number of years later, LeGuin comments on how many of her early science fiction books feature male protagonists. Even as a female author, even when writing about gender directly, she defaulted to the male point of view because that was what she was used to reading in science fiction by other authors.
On the board book front, there's the wonderful 10 Minutes Till Bedtime, which has become one of our go-to books when I'm home alone with the girls and need to cut their fingernails. Eleanor can read the whole thing aloud, and the pictures contain enough detail on each page (finding all those numbered hamsters) to keep both girls occupied until I'm done and can read them something longer. The kid in 10 Minutes Till Bedtime could be either a boy or a girl: fuzzy-haired, bright-eyed, in overalls and pajamas with pants, but in no other way gendered. Still, and although I often read her aloud as a girl, Eleanor and Isabel default to the male pronoun (actually, so do you, in your post about the book). We've written about this tendency at length before (here, here, here, and here); still, I find it striking. And I wonder, in my girl-heavy house, why it persists.