This issue has been resolved now.
The problem was not that SEF Advance stripped POST variables, the problem was that SMF bridge was sending the form to an URL without trailing slash.
And, as you might know, SEF Advance redirects all requests without trailing slash to the URL with slash to create default directory server behavior.
Then, when sent to a new page with slash, POST variables were no longer present and login would fail.
Everything can be fixed by adding the trailing slash to the URL in SMF Bridge action form, but I decided to even put the fix in SEF Advance so such URLs are supported for posting. So I added a redirect prevention if POST variables are sent.
If you download the latest version (4.8.1) you will find this issue fixed. You can just replace files: