I have two workbooks open.
In workbook A I have some UDFs assigned to cells and in workbook B I have some UDFs assigned to cells. These have already been executed, so the cells have values.
In workbook B (i.e. in the VBE) I create a new UDF, call it bar:

Function bar()

    bar = "bar"

End Function

When I then go into Excel and assign bar() to a cell in workbook B (with =bar()) and then hit Enter, the UDFs in both the same workbook and in the other open workbook (workbook A) are triggered. They are re-executed, despite already having been executed and the cells having been populated with values.

Why is this? It's bizarre and very annoying behaviour even in my tiny little practice workbooks. What if I had 100 UDFs in a workbook? As soon as I add a new UDF and assign it to a cell, all the UDFs would be triggered.

I am using Excel 2016. Thanks in advance.

So your issue is that you are placing InputBox() functions inside your UDF. While you can certainly do this, it essentially defeats the purpose of using a UDF to begin with.

Consider placing an argument inside your UDF that pulls the data from the worksheet instead of you prompting for the user's input every time recalc occurs. Or make a global variable that will remain active while the worksheet is open.

Using UDF Arguments

If you had a UDF that looked like this:

Public Function myUDF()

    Dim myInput As String

    myInput = InputBox("Type Something")

    myUDF = myInput & "!"

End Function

You could add an argument that will pull your myInput from the worksheet instead:

Public Function myUDF(myInput As String) As String

    myUDF = myInput & "!"

End Function

Which on your worksheet, would look like this:

=myUDF(A1)  'Where A1 is your new `myInput` argument

Using Global Variables

You can also use a global variable that will get your input only when you want to change it. Perhaps you can create a command button that you will press to prompt for your input, or if you only need to prompt it one time - you could use the Workbook_Open() event to set this variable - or a combination of both.

So at the top of a standard module, you could add your global variable:

Public glbVarStr As String

And then you would just run any Sub to set your global variable:

' Since this is a WORKBOOK event, you would need to place this sub in

' your workbook's code module

Private Sub Workbook_Open()

    glbVarStr = Inputbox("Type Something")

End Sub

which you would then add to your UDF:

Public Function myUDF() As String

    myUDF = glbVarStr & "!"

End Function