Can simultaneous updates and deletes on a set of tables lead to AccessExclusiveLock being taken?

You are quoting from the wrong section of the manual. That passage is from the Table-level Locks section. The lock type you are interested in is specified to be tuple. That means you need to refer to the manual's Row-level Locks section in order to find out when that kind of lock is acquired.

And in the beginning of Row-level Locks it says (original emphasis preserved):

In addition to table-level locks, there are row-level locks, which can be exclusive or shared locks. An exclusive row-level lock on a specific row is automatically acquired when the row is updated or deleted. The lock is held until the transaction commits or rolls back, just like table-level locks. Row-level locks do not affect data querying; they block only writers to the same row.

Therefore, the lock could be acquired either by Tx 1 or by Tx 2, because one is updating rows and the other is deleting rows.

Moreover, as pointed out by ypercubeᵀᴹ in a comment, your update statements are not restricted by a filter, thus each running on the entire table. When run in parallel with a delete, even a filtered one, such an update can naturally be expected to cause collisions acquiring exclusive locks.