This would convert the date field to string if and only if the account type = Prospect or Customer, else it would display the date field in the date format for anything other than Prospect or Customer.

IF(ISBLANK( Fiscal_Year End__c), 
NULL, 
IF(OR(ISPICKVAL(Type,"Prospect"),ISPICKVAL(Type,"Customer")),
TEXT(DAY(Fiscal_Year End _c )) & " " & 
CASE( MONTH( Fiscal_Year End _c ), 
1, "January", 
2, "February", 
3, "March", 
4, "April", 
5, "May", 
6, "June", 
7, "July", 
8, "August", 
9, "September", 
10, "October", 
11, "November", 
12, "December", "None" ),TEXT(Fiscal_Year End__c)))