I wonder if there is a word play between the foxes שֻׁעָלִים and the Shulamite הַשּׁוּלַמִּית? There is some similarity in sound. I looked around for some more SHL type sounds with or without guttural. Song 4:2 and 6:6 came up (pun) שֶׁעָלוּ, (= which came up from the washing). The significance seems to be nil.
But I will make something of it anyway. What are these foxes that we are to catch? They are so cute. These are destructive tendencies in each and all of us. If they are not caught, they prevent our learning and growth - not to mention the love of others.
The Academic and the Religious are both fox-filled. (Lots of recent posts - like this one from Mike Koke and others noted here.) There is one world and all the churches are in it. No context can allow us to escape our responsibilities to ourselves and to each other in that world. No label or insistent dogma will allow us to catch foxes. No claim of faith will determine a positive end without critical application - but it doesn't mean critical must be in your mission statement.
The Shulamite might get busy learning her essential unity.