There is always a context for literary interpretation. It could be biographical, historical, literary-historical, ideological, or anything else.
(It would take more work to justify this point for readings that seem merely formalist or immanent to the text itself. But I could do it.)
So the choice is not between context and no-context, but in the choice of interpretative framework.
Wars between approaches are argument about what context is the most relevant one.
"Culture wars" between canonical Western culture and feminism, gay studies, race, etc... are battles over what the interpretative context should be.
Is the "Tempest" "about" colonialism? The historical context of Shakespeare's time? (Greenblatt).
Is it about Shakespeares's own artistry? A self-reflective metadrama in which Prospero is a stand-in for the author?
Is it about the author's unconscious mind? The metaphysics of presence? Girardian mimetic desire? It will be about any of those things if you want it to be. The horizon of interpretation most relevant to us now is the survival of the planet, so maybe an eco-critical reading of the Tempest should be the trump card?
Latin American romantic novels are "about" nation-building, right? That seems to be the dominant interpretation.