Av
This is in response to her question ... in which she writes about the state of her children’s health, may they live, and she concludes with a question about what she should do regarding foods whose kashrus is not mehudar, and she thinks that this food could increase her children’s appetites. In general, hiddurim with food (as is quoted in several Torah sources) affects not only the observance of that mitzvah [of kashrus], rather since each item of food [we eat] becomes thereafter the blood and flesh of the body, which [in turn] connects itself with the neshamah, [therefore] the kashrus and refinement of the foods also influences the personality and good middos of the person eating the food. Therefore, each additional hiddur, refinement, and cleanliness of a food should be considered as an addition in the form, fineness, and refinement of the personality and middos. If this is true of adults, it applies even more to children, as their personality is developing…
According to the above, my opinion is evident: Since this is not a matter upon which one’s entire health depends, chas ve’shalom, and is only meant to add flavor to the food and to add to the [children’s] strength, a hiddur regarding food should not be dropped. Surely other suggestions and methods can be found in order to increase their appetites and improve their health, not at the expense of kashrus and hiddur.
(Igros Kodesh, vol. 18, pp. 109-110)
Elul
...Cholov Yisrael in particular has an effect on the strengthening of emuna. “Milk that was milked by עכו״ם (non-Jews) – that Yisrael did not supervise” – brings one to have doubts in emuna (chas ve’shalom), and this is easy to understand.
... According to the known story* from my father-in-law, the Rebbe (and a similar one was also printed), cholov akum awakens doubts in emuna.
(Igros Kodesh, vol. 22, p. 132)
*[There is a well-known story about an individual who came with his son-in-law, who was a big lamdan, to the Alter Rebbe in Liozna. The man complained that his son-in-law had always exhibited good conduct but recently had started to have doubts in his emuna, and the father-in-law himself had suffered greatly from this. The Rebbe told the son-in-law that he had unknowingly eaten cholov akum and gave him a tikkun (spiritual rectification) for this, and he recovered spiritually.]
(Sefer Hamaamarim Yiddish, p. 57)