Rules text does not prevent this use of the Ioun Stone
Unless a DM rules that there is a limit, casting Find Familiar from the Reserve Ioun stone provides a familiar per the spell description.
Any creature can cast a spell of 1st through 3rd level into the stone
by touching it as the spell is cast. (SRD p. 227)
Your PC's are creatures and thus qualify under "any creature."
The spell description for Find Familiar (SRD p. 149) does not impose any limit on class or race. With no specific prohibition, there's no reason not to allow it beyond a DM's preference for a particular world.
A hard requirement that you didn't address in your question is that each character in turn needs to attune to the stone in order to cast the find familiar spell. (SRD p.227). That will take at least three short rests to accomplish.
Ioun Stone Wondrous item, rarity varies (requires attunement)
How to attune the stone: one short rest per player character
Attuning to an item requires a creature to spend a short rest focused
on only that item while being in physical contact with it ... at the
end of the short rest, the creature gains an intuitive understanding
of how to activate any magical properties of the item, including any
necessary command words. An item can be attuned to only one creature
at a time (SRD p. 206)