So assuming institutions hold coins that aren't being advtanged by some softfork in the code, the owners of those coins will act in their own interest to move the coins to addresses that presumably are advantaged by the change in the code or they will intrainstitution swap to USD and remove their cuckbucks so they can buy advantaged coins elsewhere.  Or am I missing the meaning of your original question? 

 What if institutions don't allow for use of soft forked op_codes in a receiving address? 

 Then they can't receive those coins and have a reduced market they can participate in? 

 His many coins can't be received in this case?
What about pro-softfor institutions? How do they show support? 

 I think I would want to add some facts to the hypothetical to give an opinion but typically we show support by speech by running the code and speech through where we put our money.  If I'm an institution that is pro softfork and am accountable to shareholders, directors, or benefactors then I send out some missive about the proposed code, invite questions and comments, and then update the node.