Measure with an if statment?

Sure, this is fairly straightforward.  You want a DATEDIFF between [Inventory Date] and [Ignore Date].  In the case that [Ignore Date] is blank, you want to use today's date instead.  In the case that [Inventory Date] is after [Ignore Date] you want 0.

DaysOutofStockWithIgnore =  MAX ( DATEDIFF(MAX('ns InventorySnapshot'[InventoryDate]), 
                                     IF(MAX('ns InventorySnapshot'[IgnoreDate]), MAX('ns InventorySnapshot'[IgnoreDate]), TODAY())
                            ),0)

This should work (maybe with minor syntax issues. I'm not sure if you need to use MAX to get a single IgnoreDate or if you should use SELECTEDVALUE).  What I'm doing (from inside to out) is checking if [IgnoreDate] has a value.  If it has a value, use that, if not use TODAY().  Find the difference between the InventoryDate and the IgnoreDate/Today. Finally, it returns whichever value is larger: The difference between the dates, or 0.  So instead of a negative number, you see a 0.

Hopefully what I did makes sense.  If it doesn't, please ask questions.

Am I lost or is your if statement not complete?

 IF(MAX('ns InventorySnapshot'[IgnoreDate]), MAX('ns InventorySnapshot'[IgnoreDate]), TODAY())

What is it comparing against?

This is what I am using.

DaysOutofStockWithIgnore = CALCULATE(MAX(DATEDIFF(Max('ns InventorySnapshot'[InventoryDate]),if(max('ns InventorySnapshot'[OC_NSL_SPECIAL]) = BLANK(), TODAY(),Max('ns InventorySnapshot'[OC_NSL_SPECIAL])),DAY),0))