As stated elsewhere, membership of CotH is open to all hacks. The definition of 'hack' is, however, rather difficult to agree upon. Several attempts have been made, but for most of the attempts there have been some obvious (some might say embarrasing) counter-examples, and the rest have consistently failed to include everyone who actually is a hack.
The Hack Test is probably one of the more famous attempts to determine who was and was not a hack, and arguably one of the least successful ones. It actually worked quite well, for entirely the wrong definition of 'hack'. It's still around, largely for historical reasons, and because people do look for it.
More recent attempts have acknowledged that there are self-evident principles of Hackery, and attempt to reduce these to the shortest possible statement of belief. This research is currently not near completion, but it does appear that the limitations of the english language make it impossible to phrase the principles in a way that belief in them is both necessary and sufficient to be a hack. Whether this is due to limitations in the phrasing, or due to there being further factors not considered is not yet known.
Political belief is not a consideration. There are hacks from almost all (non-extremist) political beliefs, Conservative to Labour to Liberal to Socialist, as well as a large proportion of non-party or apolitical hacks.