The option to display inactive is applied to lookups other than the lookups in the entity maintenance (Item Maintenance, Customer Maintenance, Vendor Maintenance).

For Inactive Items, the lookup in Item Maintenance will always include inactive items.   The item lookup in Sales Order Entry, Purchase Order Entry, etc. will use that option to condition whether inactive items are displayed.

BUZZZZZZZZZZZZZZZZZZZZZ!  Incorrect answer.  This is the Sales Order item lookup in SO Entry.  Note it is the Standard lookup.

And here is the screen shot of Inactive being unchecked.

In addition to it not really working properly, (as bethbowers shows), why would inactive items appear in Item Maintenance Lookup if you have flagged in Company setups to not display inactive items?  That makes no sense to ignore that setting in Item Maintenance if the company is defined to exclude them. 

Ah, yes - what SHE SAID.

The entity maintenance tasks are where the inactive designation is set.  If the lookups excluded those records it would be difficult to find them if you needed to change that designation or anything else in that record.  

It would be nice to allow STANDARD not to show inactive.  And to allow new built views to include or exclude inactive as the default of company setups yet allow them to allow if needed. 

I thought those settings were for the type-ahead text matches, not ALE's?

It is both.  Lookups and AutoComplete

So the real issue, though, is that it's not working in other places, such as the SO lookup...

In my stock 2023 it works perfectly.  The suggestion would be to open a support case and they can determine what is happening with your install and if need be a defect will be created for engineering to review.