See also connected question, judaism.stackexchange.com/questions/31831/…

PS I might come later and turn this into two questions, one about milk and the other about the principle I'm asking about more in general.

Downvoter, please comment. I think that the extra stringency makes sense but am trying to understand the opinion of those who don't. Sorry if poorly phrased or structured, you could suggest edits.

It's not just about milk, but where it is I would say it's about both. Thanks for your answer below, by the way; I hope others will discuss it more with you, and I'll learn from it.

(I thought of this question after seeing opinions here judaism.stackexchange.com/questions/31762/… that raising hands in prayer is a goyishe custom, even though it is mentioned in Tanach and especially psalms numerous times. So it's interesting.)

I mean, one person speaks to Hashem out loud from their heart rather than a text, and others listen and also agree with and (silently) pray it, since all agree. I come from a Christian background and that's very normal there. My rejection of Christianity makes me definitely opposed to letting it give false influences to Jewish practice, but in my understanding this would be a fine, acceptable, and very Jewish sort of thing to do (except that by custom I don't see it).

Hm, makes sense. If things are mixed on purpose but without bitul in mind, and the consumer doesn't know whether that happened... when could a Jew keep in mind that if it had happened it would be nullified for him or her?

Thanks. With your first paragraph, that's what I meant by 'after the fact'... it has to happen by accident. The question I have is how careful you have to be in advance that such things don't just happen to occur, either by accident in your own place or by an unknown hand in the production process.

There are mentions of lifting hands in prayer in Tanach, especially the psalms. How is it the manner of gentile prayer if there's this precedent?