Deadlock between two non-related tables
Looking at a subset of the deadlock information:



This shows that session 342 is currently executing line 47 of the stored procedure dbo.SP2, which is a DELETE statement on dbo.Table2.

Somewhere prior to that in the procedure, this session has already acquired an eXclusive (key) lock on dbo.Table1.  Based on the non-zero "log used" value, it seems like this procedure does some writes to dbo.Table1, thus acquiring the X lock and creating the potential for deadlocks.

The takeaway here is that the deadlock XML is only showing you the currently executing statement (Erik Darling has some great demos of this and other confusing things about deadlock graphs on his blog).  It appears that there are multiple statements being executed in a transaction in this stored procedure.

Another possibility is that there is a trigger on one of more of these tables that's causing more locks to be taken than what is obvious from the T-SQL statements themselves.




  Also, if I had the FK, why should need check the PK in table1 if I am just deleting from table2?


You're right, even if the foreign key existed on Table2, locks on Table1 would not be required to delete rows from Table2.  Locks would be required if the FK was defined "backwards" and cascading deletes were enabled.