Your feelings are correct. That is not right. The exhaust should not be making hard contact with anything and only touching exhaust hangers.
That is wrong by being against both the transmission crossmember and the transfer case. I'm going to say that should be redone. Any decent exhaust shop will laugh at that work and redo it correctly.
It's not unsafe, you can drive it to the exhaust shop. It is just low quality work. And direct contact to the transfer case would make it run hotter after a long drive. I would not recommend a 200 mile road trip at highway speeds, the transfer case oil would likely get pretty warm.