There is 2 explanation to this. He was wearing gloves or the sacrifice of black widow
I think it might be becuae horkeye did the sole for a sole (sorry for spellings?)
I still hold this is an issue only with the power stone.
Because it is basically infinite energy concentrated into a stone.
The reality gem went 'inside' jane foster, nothing happened to her.
^ except she's dying because of the stone
^Not blowing up and becoming a live bomb like the collectors servant.
Hawkeye can hold the infinity stones because he is the one in possession of the soul stone and that makes him a powerful being