Mishna said in AZ 35b:
The following articles of heathens are prohibited but the
prohibition does not extend to all use of them: milk which a heathen
milked without an israelite watching him, their bread and oil - Rabbi
and his court permitted the oil
The problem with milk is related to mixed non-Kosher species milk. The problem with bread is related to mixed marriage. Two different concerns. The Pat Palter seems allowed in Gemara in certain conditions, e.g. when Israel's made bread cannot be found, far from the city. A discussion between Rishonim, based on contradictory suggiot is emphasized Shulchan Aruch YD 112, 2. Some Rishonim allowed only Pat Palter in special condition only, and some others are allowing all pat palter (we don't want to give a comprehensive explanation) . But following one opinion, the prohibition is entire in some cases, no event cancelled it.
Here concerning pat palter, we can speak about leniency and stringency. Stringency is strongly supported by lecture of the Gemara in AZ 45-47.
But concerning milk, the prohibition was for a fear of unclean animal's milk mixture(1) The fact that milk production is nowadays a gigant industry generated new conditions in which no doubt can subsist concerning an eventually mixture of unclean animal's milk into the cow milk. However, as @Yishai mentioned, the Rama (in YD 115, 1) wrote that if there was no Israel from the beginning until the end of milking, despite that the non-Jew has only clean animals in his drove, we prohibit because of Chalav Akum. In other words, there is cases of prohibition without risk of mixture. We found this case in Mordechai (quoted in Bet Yossef) and SMAK. But Bet Yossef read in Mordechai that this case also regards unclean milk from an other place. But most poskim soon this Mordechai as describing a global Gzera, somewhat enacted which cannot be canceled despite changes in reality. See Aruch Hashulchan(2). Indeed, the orthodox communities I know (outside from America) continue the Cholov Shamur Practice.
Following the last view, milk and bread are involved in similar enactment, we can expect that the stringency or leniency in both is expected. But it is not linked with the same texts in Rishonim. And the issues are differents.
In conclusion Chalav Nochri and Nochri Bread have a similar link to industrialization of human society.
(1) Gemara AZ 35b
Why should we feel concern about milk [that it is prohibited]?
If on account of the possibility that there may have been a
substitution [of animals], [the milk of] a clean animal is white and
of an unclean animal greenish in colour! If, on the other hand, it is
on account of the possibility of a mixture ...
(2)Here is the words of the Aruch Hashulchan YD 115, paragraph 4.
ואין לשאול דבאין דבר טמא בעדרו למה לנו שיהא הישראל יושב מבחוץ והרי אין
שום חשש בזה, אמנם כתבו הראשונים דכל שהישראל לא ראה החליבה כלל והיינו
שגם מבחוץ לא ישב, אסרו חכמינו זכרונם לברכה בכל גווני דסתמא תנן במשנה
חלב שחלבו עובדי כוכבים ואין ישראל רואהו אסור. כן כתוב במרדכי ובסמ"ק
וזה לשון השערים סימן פ"ב חלב שחלבו ואין ישראל רואהו אפילו אין בהמה
טמאה בדיר אסור דלא ליפוק חורבא מיניה ופורץ גדר ישכנו נחש. כך כתב רש"י
עד כאן לשונו. וכך כתוב באיסור והיתר הארוך סימן מ"ה וזהו דעת הטור
ורבותינו בעלי השולחן ערוך וגדולי האחרונים הש"ך והט"ז והב"ח והדרישה ורק
הקילו בהשמירה דהייהו שדי בישיבה מבחוץ כמו שנתבאר וכן די ביוצא ונכנס
ולא מיבעיא ביוצא ונכנס למקום החליבה ממש אלא אפילו בישיבתו מבחוץ הוא
יוצא ונכנס ויושב לו מבחוץ (ש"ך סעיף קטן ד') ודי בזה.
He seems to understand as almost unanimously admitted that the prohibition has a global spectrum which can be modulated concerning the way of custody but not canceled.
(3) See Gemara AZ 35b concerning pat palter outside of th town.
אפי' למ"ד פלטר עובד כוכבים ה"מ בשדה אבל בעיר לא משום חתנות
The only reason to separate hurbain zones from lands is Chatnus. About oil too there is a similar statement (36a):
אלא דניאל גזר עליו בעיר
At some step Gemara said Tha the first version of oil enactment was in hurban zone only. And Rashi said that the difference between the two places is Chatnut.