How do prevent TextWrangler save alert (This file appears to have been modified) on Mac?

Here is a workaround: Turn off "Automatically refresh documents as they change on disk" in Preferences->Application.

It could be an OS related issue - TextWrangler is no longer supported on macOS 10.13. according to Rich Siegel of Bare Bones Software, Inc.:

The version of BBEdit you're (both) using is out of date, and is not supported on macOS 10.13.

TextWrangler is BBEdit now.

TextWrangler was an all-purpose text and code editor for macOS, based on the same award-winning technology and user interface as BBEdit, our leading professional HTML and text editor.

TextWrangler is now part of BBEdit. We have sunsetted TextWrangler, and we encourage anyone not already using TextWrangler to download and use BBEdit instead.

If you are an existing TextWrangler customer, it’s time to switch to BBEdit. We promise that you will feel right at home, because the two products are identical in every way that you’re used to. And you still don’t have to pay anything, unless you want to support us by buying a license.

TextWrangler is not compatible with macOS 10.13 (High Sierra). Please install and use BBEdit instead.

https://www.barebones.com/products/textwrangler/