Did you notice something different in this picture?
The way the Uzumakis hands are in a formal folded clasping position while the Senjus are not?
This is usually the depiction of Shinto priests/monks (Shinshoku) in art and photography
(Shinshokus btw are allowed to marry and have children)
A Shinto Priestess(Miko) and Mito Uzumaki
The distinctive posture of the hands in the initial panel compared to the Senjus in the right are indicative of the clerical/priestly nature of the Uzumaki Clan.
And wasn't it said by Jiraiya that Rikudou Sennin was a priest/monk who preached Ninshu during a time of endless war?
Factions and Families (non-shinobi) or clans must have existed during that time because war is conducted by opposing factions, and in medieval era Japan wars are made by opposing families/clans
I think Rikudou Sennin was part of the Uzumaki Clan(non-shinobi) even before he discovered ninjutsu, it was only when he discovered the nature of chakra and ninjutsu that he taught it to his clan-members (Fuuinjutsu) thus becoming the Uzumaki Shinobi Clan of the present era, afterwards Rikudou set out on his own and travelled to teach ninjutsu and the way of peace all over the world.