Is there a gender-neutral prefix for "parent"?

The prefixes "patr-" and "matr-" refer, respectively, to father and mother--e.g., a patriarch is a father who rules a family, and a matrilineal society is one where property is passed from mother to daughter.

Is there a prefix that refers more generally to "parent"?

Solution 1:

The answer is yes, and that prefix is parent.

From MW;

Origin of PARENT

Middle English, from Anglo-French, from Latin parent-, parens; akin to Latin parere to give birth to

Solution 2:

"Parr-" seems to be the general term to refer to either parent, at least insofar as the term "parricide" vs. "matricide" or "patricide".

Parricide: Characteristics of sons and daughters who kill their parents

Understanding Parricide: When Sons and Daughters Kill Parents

I haven't done an exhaustive search to see if this prefix is used in any other contexts, though.