Looking for a word that denotes both brothers and sisters without gender connotations (gender neutral), in a similar fashion as parents for father and mother.
It sounds like you're looking for one of siblings (as in brothers and sisters), offspring, or children (as in sons and daughters).
Each of two or more children or offspring having one or both parents in common; a brother or sister.
Possibly sib (OED):
chiefly Zoology A brother or sister; a sibling.
In my opinion, the answer siblings seems to be the most terse yet adequate way to express this phrase. Here are my reasons:
- Siblings denote live, closely related beings. However, there is a glitch! Mother and father are not genetically related, while brother and sister denote genetic relationship. Possibly a more accurate, yet less popular, answer might be family members.
- Connotatively, a better descriptive sentence might be “Aunt and uncle are to family as brother and sister are to siblings”. Or “Mother and father are to family as brother and sister-in-law are to marriage”.