The Shulchan Aruch says the during aseres yemei tshuva one who eats pas akum(palter) during the year should refrain during these days.
Does this extend to those who are lenient with chalav Stam?
R' Dovid Feinstein rules that chalav stam in the US is permissible me'ikar hadin year-round, so it is not comparable to pas palter and one need not be strict to the same degree of pas palter. However, he does maintain that chalav Yisrael is ideal, so it seems like he might consider it a reasonable optional practice to undertake during the aseres y'mei t'shuva.
By contrast, R' Doniel Neustadt cites the Sha'ar HaTziyun (609:1) and the Igros Moshe (OC 3, 12) as saying that "during the Aseres yemei teshuva we should be stringent when it comes to all questionable issues." R' Neustadt writes that consuming non-chalav Yisrael dairy in the US is a controversial leniency, and he rules that, even if one is lenient year-round, "it is not appropriate to rely on this leniency during the Aseres yemei teshuvah."