Ignore Mack, he is just a waste of oxygen and currently holds the site record for number of times he has been kicked off. Just keeps coming back under different names.
In any case, your real answer is:
You have full rights of tenancy until your lease is ended. As such, unless there is a provision in your lease requiring you to allow showing, you are under no legal obligation to do so. The fact that the landlord may, or may not, lose a day or so in 'showing time' is not your problem.
However, keep in mind that you may be at a disadvantage when it comes to getting your deposit back, so you might negotiate some agreement.... you will allow showing of property in return for a full return of your deposit. Allow the landlord in early to see the condition of the unit to assure them that there are no damages. Or, if you don't want to do that, be sure to take LOTS of pictures (video preferably) of every room, closet, appliance, carpet, etc. on your final day. Do it as the last thing you do before leaving.