$ join <(sort file1) <(sort file2)
ID1 123 C T ...
ID2 234 A C ...
ID3 232 G T ...
ID4 344 A C ...
If you want keep the order of file2
$ join -1 1 -2 2 <(sort file1) <(cat -n file2 | sort -k2,2) | sort -k3,3n | cut -d' ' -f1-2,4-
ID2 234 A C ...
ID3 232 G T ...
ID1 123 C T ...
ID4 344 A C ...