The modulo parity party
Python 2, 68 67 66 bytes

-1 byte thanks to Mr. Xcoder
-1 byte thanks to ovs


x=input()
for j in x:k=sum(i%j%2for i in x);print(k&lt;len(x)-1)+0**k


Try it online!

Returns 1,0,2 instead 0,1,2.