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This is actually a server issue. Let me explain, it's a slightly convoluted :)

The Reduce MIME Type Security Risks adds a .htaccess rule which instructs the web server to send a "no sniff" HTTP header with every request. All modern browsers respect that header and will not try to guess the MIME type (media content type) of a file sent to them if the MIME type is not sent with the content.

Here comes the server bit. Web servers have a MIME type registry file. It tells them which files are which MIME type. This allows you to rename a JPEG file to foobar.bmp and have the server figure out that it's not a BMP file, it's a JPEG file, and tell the browser to parse it as a JPEG file by sending the correct MIME type. If your server's MIME type registry is missing the mapping for WEBP files then the web server does not send a MIME type and the browser has to figure it out by itself.

So here's the problem. You told the browser not to figure out missing MIME types but your server didn't send a MIME type. Therefore the browser puts its hands up in the air and says "I don't know what to do with this file!" and does not display it.

One possible fix is adding the following code to the .htaccess Maker's area for custom code to add at the top of the file:

<IfModule mod_mime.c>
  AddType image/webp .webp
  AddType image/webp .WEBP
</IfModule>

If your web server has the Apache MIME module enabled your images will work properly. If this doesn't work you need to temporarily disable the reduce MIME type security risks rule and ask your host to add the correct MIME type mapping for webp images.