Open two GIT branches in two separate IDE instances?

After making the two clones as David Deutsch suggested, I recommend picking one as primary and creating a symbolic link to the .idea directory from the secondary clone to the primary clone. This way you will have the same config in all clones.

ln -s primary_clone/.idea secondary_clone/.idea

This assumes you use the .idea project config format and that you do not check config to the repository (in that case you are obviously all set from the get go)

it mostly works, only sometimes Idea prompts you with dialog box to reload other projects if you change some setting in the currently active one. You can refuse, though.

You are correct: there is only one active branch at a time. The best you can do is to clone the repository twice on your local machine into two different directories, and then simply open up the appropriate directory in each IDE instance.