Well, I keep regular backups of the whole site so instead of fiddling with the plugin I just restored the whole thing and problem disappeared. Then I edited the version number from 2.7 to 2.7.1 in order to get rid of the plugin update reminder. So it is not a big deal and anyway any changes I made are my responsibility and the risk is mine, not yours especially that you do not charge for the plugin. I have created another backup and then run an upgrade to 2.7.2 and this seems to work all right. No issues, so big thanks for keeping up a good job and for very fast response to my post.
My site: https://blog.pibyk.org
Theme: Moesia
Other plugins: 27 of them, but nothing really tricky.
Symptoms: being logged in as admin on the home page I could only see the header picture and site title and subtitle, no admin top menu, site menu was visible, side bar was invisible (so no meta, no log-in etc.) and only title of the last post was visible. The title was click-able, click directed to the post text, but nothing else was visible. Footer was also not visible. Back-end worked as usual, pages (accessible from top menu) were working in order.
Might be some sort of conflict between the theme and plugin code as Moesia gave me already some headaches of similar nature.
If I can be of any more help then contact me through my site (contact form) and I will try to answer all questions in more detail.