"Blatantly obvious" is at best a well worn cliche. Strictly speaking it is not redundant, because blatant indicates an annoyingly assertive sound.

What does blatantly obvious mean?

adjective. You use blatant to describe something bad that is done in an open or very obvious way.

How do you use blatantly in a sentence?

He returned her gaze, hoping she would back off, but she continued to blatantly stare, then finally dropped the mask. Deborah spent most of dinner staring blatantly at Jackson, vying for his attention whenever possible.