Kosher Wine (Mevushal & Stam Yeinam) (סתם יינם)
Grape wine and grape juice have their own kosher rules. 'Mevushal' (heated) kosher wine can be handled by anyone; regular kosher wine should be handled only by observant Jews once opened.
Because wine once played a central role in idol worship, the Sages ruled that grape wine handled by non-Jews ('stam yeinam,' meaning ordinary non-Jewish wine) may not be drunk. But kosher wine that has been 'mevushal' (heated/cooked during production — many authorities include modern flash-pasteurization) is no longer affected by this, so anyone may pour or handle it.
An event or restaurant where non-Jewish staff serve the wine.
Use mevushal wine — anyone can open and pour it without affecting its kosher status. Why: Heating the wine changes its status so it's no longer treated like wine that could be used for idol worship, which removes it from the original concern. That's why so much kosher wine is made mevushal.
Regular (non-mevushal) kosher wine at a mixed gathering.
Once it's open, only an observant Jew should pour or handle it. Why: Non-mevushal wine keeps the original concern, so a non-Jew handling the open bottle makes it forbidden to drink.