Using exiv2
I was not able to find a way to get exiv2 to output to stdout -- it only wants to overwrite the existing file. You could use a small bash script to make a temporary file and get the md5 hash of that.
image.sh:
#!/bin/bash
cat <&0 > tmp.jpg  # Take input on stdin and dump it to temp file.
exiv2 rm tmp.jpg   # Remove EXIF tags in place.
md5sum tmp.jpg     # md5 hash of stripped file.
rm tmp.jpg         # Remove temp file.
You would use it like this:
cat image.jpg | image.sh
Using ImageMagick
You can do this using ImageMagick instead by using the convert command:
cat image.jpg | convert -strip - - | md5sum
Caveat:
I found that stripping an image of EXIF tags using convert resulted in a smaller file-size than using exiv2. I don't know why this is and what exactly is done differently by these two commands.
From man exiv2:
rm        Delete image metadata from the files.
From man convert:  
-strip        strip image of all profiles and comments
Using exiftool
ExifTool by Phil Harvey 
You could use exiftool (I got the idea from https://stackoverflow.com/a/2654314/3565972):
cat image.jpg | exiftool -all= - -out - | md5sum
This too, for some reason, produces a slightly different image size from the other two.
Conclusion
Needless to say, all three methods (exiv2, convert, exiftool) produce outputs with different md5 hashes. Not sure why this is. But perhaps if you pick a method and stick to it, it will be consistent enough for your needs.