I've heard both phrases in everyday speech, so there's little doubt in my mind that the answer is both. I suspect, though, that one of these phrases is more the original than the other, and the other sprang out of it from mis-hearing.
Glaringly obvious seems essentially redundant; the word obvious occurs in the definition of glaring in the three dictionaries I looked at.
Blaringly obvious is less favored by, say, Google, but actually describes the obviousness, as opposed to repeating it.
Are these two statements identical? Is one the forebear of the other?
- It is difficult to resist the urge to fix these glaringly obvious errors.
- It is difficult to resist the urge to fix these blaringly obvious errors.
What about this third? Is it preferable, or does it change the meaning?
- It is difficult to resist the urge to fix these glaring errors.
Best Answer
I disagree with your interpretation.
Glaringly obvious describes that the thing [metaphorically] glares at you. It's a sight-based metaphor. A similar idiom is blindingly obvious.
Blaringly obvious is a combination of glaring and blinding. If something is blaring, it's screaming at you, so while it does have much the same connotations as glaring and blinding, it's a sound-based metaphor and less suited for seeing what is obvious.
I suspect that the original user misused both glaringly and blindingly and ended up with what is effectively a Spoonerism. Since then, it's either been used deliberately as an off-beat metaphor (sound-based rather than sight-based) or it's an eggcorn.