Can I de-activate the plugin withouth disrupting the website?

I already posted a support request concerning menu items not working with https.
Now I’m really concerned since I tried to de-activate the plugin and the html pages arrive disrupted if I ask them via https. I hope the solution may be in something else than restoring a db backup! 🙁

Thanks in advance!

The page I need help with: [log in to see the link]