I want to be able to have two instances which are completely independent in the sense that I can be working on two separate unrelated projects in different folders without any i
Although clicking on the Spyder icon will not allow you to open two instances, you can open a second instance by simply going to the folder where spyder.py is and running spyder.py from the command line.
Further, you could make an icon for your desktop that simply runs spyder.py from its location. However, I don't know how multiple instances will affect user preferences if Spyder has those.