Gender neutral terms to call a parent

Fom (father + mom)
Parry (like "parent" but with a more "mommy/daddy" feel)
Baba
Cenn (short for Old English cennend, a neutral term for parent)

There's a good list on this article:
Gender Neutral Language (Wikipedia)

For pronouns, one that I like is "hen" which has actually been officially adopted in Sweden as a gender neutral pronoun. However, that is obviously a personal choice and up to them entirely.

 

I've heard kids calling their biological father "Maddy"

 

Personally, I started calling my parents by their names when I was in grade school, and I think it's done great things for our relationship.

 

i think youll find this to be useful Gender Queeries

 

I'm glad I came across this because my partner is genderfluid and we actually have tried to figure out what they would be called as a parent

 

I've seen many kids that call their parents by their first names. That could always be an option...