At what stage does a born-Jewish messianic Jew's presence at and/ or participation in an Orthodox synagogue's kiddush make wine 'Yayin Nesech'?
Wine becomes yayin nesech when it is open and then is handled by a non-Jew or by a Jew who violates Shabbat or participates in avoda zara. "Messianic Judaism" could certainly be considered a form of avoda zara as discussed in other places on this site. So if the person touches an open bottle of wine, that wine would become prohibited.
If the wine is mevushal, though, there is no issue of yayin nesech because the wine is not considered fit for avoda zara libations. My experience is that most shuls use wine that is mevushal to get around the problem of someone attending kiddush who does not keep shabbat. Therefore, I would assume that your shul probably is also using mevushal wine and there is no problem. This is easy to check by looking at the label of the bottle.
You are all incorrect. Wine only becomes nesech when used for a ritual in the name of an avoda Zara. However when a goy moves the wine it becomes yayin stam. There is a HUGE difference, yayin nesech is assure b'hana (forbidden to derive benefit), and nesech is forbidden on a biblical level. Yayin stam is a rabbinic ordinance but the prohibition only forbade consumption of the wine, however the rabbinate never forbade stam for benefit.
Wouldn't a "Messianic Jew" be actively be participating in idolatry, therefore there use of wine in any regards be for idolatry thus no longer be kosher? Maybe I am thinking too much into this but would venture to guess that anyone practicing idolatry would make kosher wine non kosher once touched.