Blatant means glaringly conspicuous—in other words, glaringly obvious. So, because obvious is included in the meaning of blatant, the common phrase blatantly obvious is redundant.
Examples
In each of these examples, the sentence would not change meaning if blatantly obvious were replaced with either blatant or obvious:
The fact that the one was a hairline decision and the other, last Sunday, blatantly obvious, is neither here nor there. [Telegraph]
It’s blatantly obvious that they’re just men in rubber suits, and their voices are also rather comical, sounding like a man who’s gargling with treacle. [Shadowlocked]
In our view, the market has been overlooking blatantly obvious good news, such as strong oil prices and rising oil demand forecasts. [Street Insider]
