Interesting. I was not aware of the existence of GEMA until I read this thread. As far as I know, similar societies exist in Austria, in Switzerland and in my own country, Italy, and possibly elsewhere too.
In Italy it is called SIAE (Società Italiana degli Autori ed Editori = Italian Society of Authors and Publishers) and seems to be quite similar to GEMA (a few legal details set aside).
The basic concept for SIAE is simple: they collect rights whenever a work of a member author or publisher is performed or used in some way publicly (meaning that it is being profited by an audience who didn't buy it) and periodically the collected amount is divided among the members. Then, many aspects of the practical implementation of this principle are questionable indeed and are repeatedly questioned, but this a second approximation point.
Note that this has nothing to do with censorship: neither SIAE nor, I think, GEMA has any right to decide what can be performed and what cannot or when or where. SIAE is also not involved in age-related limitations (like movie rating or PEGI/ESRB or similar).
In general, I think it is possible to say that in Italy censorship, which was a problem a few decades ago, is now a relatively minor problem. At least as far as State-imposed censorship is considered; there is a serious problem of self-imposed censorship (by journalists, news agencies and so on) about topics which can be addressed and topics which should be ignored, about the way to present specific topics and so on. But this a rather different matter, involving different parties and agendas.
Also, SIAE -- and probably GEMA -- action is not directly related with taxes: that money is not a "tax" and does not go to the State, but to the authors and publishers as a group (at least in principle, then, as I said, the actual implementation is often a bit too murky).
That said, the very existence of this kind of 'authorities' is questionable; their origin can be in part traced back to the privileges granted to trade guilds by Medieval states and for another part sits on a very outdated concept of trace and of "author's right" (a vvvvvery murky topic in itself!).
So, I definitely agree with @ArcticuKitsu that this approach is to be opposed, but it is also important to aim at the right target, which is not 'political' (or only in a very general and generic sense), but rather (socio-)economic.
