This practice is usually called "proof-texting" [1] and perhaps surprisingly it's not confined to one particular kind of Christian. For example, the very conservative evangelicals I grew up with were extremely anti proof-texting and decontextualized reading, to the point that they rarely read from the Bible (in church or otherwise) unless they're reading a whole chapter. On the other hand, the conservative evangelical Dwight Moody is often accused of promoting exactly this hermeneutical approach. In my experience, a certain class of the "reformed" are often guilty of it.

To be clear, I certainly think the people I grew up with were guilty of their own particular hermeneutical weaknesses, this is just about proof-texting.

[1] https://en.wikipedia.org/wiki/Prooftext

[2] Can't find a ready source for this, could be the result of some infighting.