Excel 2010 always does "updating cells" before it runs my macro. How can I turn that off?

Here is the file.

To replicate:  Go to the "Scriptures" worksheet.  Then click on any of the buttons at the top of the columns, e.g. A, B, C, D etc.

The macro is designed to sort the spreadsheet by that column.  It used to work just fine, but now it takes 15-20 seconds while it does "updating cells".
Scripture-140824-trying-to-fix-the-updat

I think the file name was truncated when I uploaded it previously.

It had been set to "Automatic" calculation.  I tried changing it to "manual" just for fun;  it didn't help.

Here's the file uploaded with a shorter name.
Scripture-140826.xlsm

Any luck downloading that file?  Can you replicate the "updating cells" problem?

Thanks Zack.

Just got back from vacation.

Since this has been open a long time, and your answer seems very thorough, I'll close this question without studying it carefully for now.  I'll look at it tomorrow in detail.

I really appreciate your help.

Thanks!