Zack,
thanks a lot for your fast reply and your offer to help, that is much appreciated. However I am glad to share with you that 1) Cloudflare caused the problem and 2) the support guys from Cloudflare solved the problem right away (their support, on my opinion, is superb!).
The solution to the problem was to switch off two Beta features in the settings, which were minifying CSS and JS, as well as asynchronously loading Javascripts. After that was done, the Calendar Plugin works just fine.
Thanks again for your help!
Steffen