I'm feeling some dissonance between the stated policy of not-so-much-doctrine and the content of questions I see. To begin with, every time I see the term 'OT', I cringe. I appreciate that not all Christians are even aware of the insult implied, but it's there nonetheless.
I appreciate that it's not reasonable to ask that no one ever use the term OT, let alone to go on an editing spree eliminating it.
Then, consider, for example: a question about 'sensus plenior'.
This is a fundamentally Christian approach to the text. The question is sort of a meta-question to a number of questions which start from the assumption that the Hebrew Bible contains prophetic references to Jesus. Which, of course, is a mainstay of Christian doctrinal interpretation.
I haven't found any examples of conflicts going in the other direction. I could, for example, imagine someone getting upset over quotations from "Canaanite Myth and Hebrew Epic" by Frank Moore Cross.
Or, in another direction, I spotted a bit of comment dialog (which I can't find again) about being careful to avoid offending some people's sensibilities with profane language. I wonder, then, what would happen if Job 31:10 came up? (This might be a whole other question.)
One might imagine an alternative: a question framed explicitly as 'Do Christians read verse X to say Y?'. Would that be on-topic here? Or does it belong over there?
After reading Caleb's extensive answer, I wanted to explain a bit more about why I'm writing this.
I start from a hypothesis: I'm a member of a category of persons whom you would like to have around here. I'm an amateur scholar of Biblical Hebrew / Hebrew Bible. My tradition is Jewish, but my studies are primarily text-critical/modern.
Without descending into a pit of political correctness, I'll merely remind you that people are comfortable when they don't feel invisible. Some things that I see around here make me feel more visible/comfortable. Some less. There's a tipping point out there at which people like me won't feel inclined to show up. 'OT' is a negative. Explicitly owning ones assumptions is a positive. I'm not proposing that you 'solve' this 'problem' by imposing any particular rules on anyone. I'm just trying to communicate some sense of how the different flavors of content strike me.
I think that this is a very hard problem, since the people who show up to ask are not, reliably, going to be very sensitive to this topic. Chasing people away because they enter questions that have unstated doctrinal assumptions doesn't feel very friendly, but a front page entirely composed of questions about how the Hebrew Bible prophesies Jesus isn't going to keep people like me around, either.