The principal difference between kosher wine (or grape juice) and non-kosher wine (or grape juice) is that the kosher wine must be produced and handled only by religious Jews. However, once the wine or grape juice has been cooked (“mevushal”), it may be handled by anyone, including people who are not Jewish, and it will still remain kosher. Pasteurization may be sufficient to be considered “cooking” for this purpose.
 
Note Many good-quality wines are NOT mevushal and when those bottles are opened must not be handled by anyone who is not a shomer Shabbat Jew.