Are there any legitimate ways to watch NFL season on Android without cable/satellite subscription?
The NFL keeps a tight rein on its broadcast rights. Further, the outfits that ponied up those huge payments for those rights are not going to be happy if there is a cheaper alternative. So, no, there is not going to be a way to watch live NFL games without subscribing to cable or satellite.

If you're okay with watching games after the fact and you have an Android tablet, there's Game Rewind.

Things may be different outside the U.S. Using a proxy to bypass such limitations skirts the edge of legitimacy (in my opinion).