You’re right - at present, the only available OS for the Fairphone is Android, for reasons that have to do with the chosen Mediatek chipset (source code not publicly available) You can, however, use your phone without using any google applications (app store, calendar &c &c). But even with the basic open source Android OS installed you’re to an extent under ‘google control’ since the company undoubtedly strongly influences the development of Android.
As I understand it, the FP team is actively working towards a solution, so new phone generations may offer the option to choose among OSs. See this thread, for instance: Closed Poll: Future Fairphone OS Development
However, even with a completely independent OS you cannot use a phone (or a PC) without, to some extent, becoming dependent on or ‘supporting’ transnational giants working for profit. There will always be servers running Microsoft or Apple software. There will always be operators doing shady business in third world countries. We cannot at present escape capitalism.