A very good question, which needs to explore what is the prohibition of "Stam Yenam", I assume that you have a basic knowledge concerning the fact that wine of non-Jews prohibited consummation has to do with Idolatry and intermarriage. We can add that most non-Jew in wine-producer countries are not Idolater at all. I will try to explain the question and to give an partial answer based on Rambam, for clarity and brevity.
The wine of a non-Jew who is not idolater: See Rambam Kedusha, Maachalot Asurot, 11, 7:
וְכֵן כָּל גּוֹי שְׁאֵינוּ עוֹבֵד עֲבוֹדָה זָרָה, כְּגוֹן אֵלּוּ הַיִּשְׁמְעֵאלִיִּים--יֵינָן אָסוּר בִּשְׁתִיָּה, וּמֻתָּר בַּהֲנָיָה;
The consummation, but not the benefice from this wine is prohibited, not as Stam Yeynam from idolaters who is prohibited even from benefice.
The Kessef Mishne cited a Responsa of Rashba explaining the Psak of Rambam concerning wine of non idolators non-Jews:
וכתב הרשב"א דטעמא משום דגזירה ראשונה לאסור שתיה בלבד היתה ומשום בנותיהן אבל איסור הנאה שגזרו ב"ד שלאחריהם ומשום חשש ניסוך לא גזרו אלא בעכו"ם עובד ע"ז אבל בשאינו עובד לע"ז לא היתה גזירה ..... וכדגרסינן התם עלה דההיא רב יהודה שדר קרבנא לאבידרנא ביום אידם אמר ידענא ביה דלא פלח לע"ז ... אלמא כל שידענוהו שאינו עובד עכו"ם אינו בכלל גזירות הללו ... ומ"מ כל שאסרו משום חתנות אף הוא אסור בו שהרי הוא בכלל איסור חתנות ולפיכך יינו אסור בשתייה כשמנו עכ"ל:
He says basically that there are two commitments. The first concerning wine and some other foods, in way to avoid intermarriage, it is a eating prohibition only, the second when it can be a doubt if the wine has something to do with idolatry, it is a benefit prohibition.
In order to continue to reasoning with your question, we are now going to cast aside the second commitment.
they don't have any direct relation to the customers, so there is no reason a jew will get married with them.
This sharp question is relating with the fact that it seems that Chachamim apply different rules concerning the non-Jew bread prohibition; you assume also that the commitment should be equivalent for bread and wine, concerning the intermarriage-linked commitment. See Rambam, Kedusha, Maachalot Asurot, 17, 12:
אַף עַל פִּי שֶׁאָסְרוּ פַּת גּוֹיִים, יֵשׁ מְקוֹמוֹת שֶׁמְּקִילִין בַּדָּבָר וְלוֹקְחִין פַּת מִן הַנַּחְתּוֹם הַגּוֹי, בִּמְקוֹם שְׁאֵין שָׁם נַחְתּוֹם יִשְׂרָאֵל; וּבַשָּׂדֶה, מִפְּנֵי שְׁהִיא שָׁעַת הַדֹּחַק. אֲבָל פַּת בַּעֲלֵי בָּתִּים, אֵין שָׁם מִי שֶׁמּוֹרֶה בָּהּ לְהָקֶל: שֶׁעִיקַר הַגְּזֵרָה מִשּׁוֹם חַתְנוּת; וְאִם יֹאכַל פַּת בַּעֲלֵי בָּתִּים, יָבוֹא לִסְעֹד אֶצְלָן.
He explain that despite the prohibition to eat non-Jew bread, in some countries, they permit to eat bread from the baker if there is no Jew-bakery. The reason is that it is very difficult to deal without bakery. But despite this leniency, the home-mad bread remains prohibited because of the basis of the commitment, which is to avoid intermarriage. If we eat their home-made bread, we would eating at the non-Jewish home, a thing that lead to intermarriage.
This leniency is reported for bread and not for wine. Even for bread, it is not an absolute leniency.
Concerning the commitment, it begin with wine. See Gemara Shabbat 17b:
Rather [say] they decreed against their bread and oil on account of their wine, and against their wine on account of their daughters, and against their daughters on account of 'the unmentionable,' and [they decreed] something else on account of some other thing.
For wine, Rashi says in AZ 36b:
משום יינן. שהיין בוער בו ומביאו לידי בנותיהן:
because the wine is boiling in him and leads him to their daughter.
For this reason, some Rishonim (e.g. Tosfot Shabbat 17b think against Rambam, that the wine prohibition is already a benefit prohibition, no matter with idolatry).
So, wine is different from bread from his need which is lower and his__ danger which is bigger__. Despite that the risk is not directly to marry with the daughter of the worker of the winery, a general risk of intermarriage persists.