In a posting in November 2013, I argued for a ‘translation service’ from CalDAV to IMAP, i. e. a service that provides a CalDAV interface to the user, but transparently stores the calendar entries in any (read: third-party) IMAP account configured by the user.
Now, soon after my posting I stopped looking for solutions, as other RL matters popped up. However, the need for a synchronized calendar across different devices and family members still exists. Therefore, I restarted my search for a solution.
I am still living under the assumption that you cannot trust the big service providers, as they know already too much about you. As a pragmatic solution, I was looking for a provider that is specialized in calendars and at least tries to look and act trustworthy.
The first provider I came across was FastMail, a mail service formerly owned by Opera. They offer a calendar service as well, but it seems to be in beta stage right now and is only available for the more expensive business plans.
The solution I finally settled for a more extensive testing is Fruux. It is a German start-up and the web interface is modern but still acceptable to use. They offer, like Memotoo, different plans, where the for-free one allows you to synchronize two devices: Both devices get different credentials, so it is easy to lock out a device in case it gets lost or stolen. You can get an URL to a read-only version of your calendar if you want to read it from more devices without paying. Paid plans provide you with more calendars, more devices, more team/sharing features etc. The company seems to be committed to open source and there is an API if you want to build your own services.
The biggest (only?) drawback is that the infrastructure is hosted in Amazon's cloud, although it is supposed to be located on an European server.