An ideology is a set of one or more "beliefs" (what I call "modules"). I make a distinction between a monomodular (MM) ideology and a polymodular (PM) ideology. Examples of monomodular ideologies are atheism, polytheism and pantheism, which offer only one module. A follower of a monomodular ideology is someone who adheres to the module offered by that ideology. For example, and atheist is someone who thinks that nothing is divine, a polytheist is someone who thinks there are multiple divinities and a pantheist is someone who thinks everything is divine. A polymodular ideology offers multiple modules: examples of polymodular ideologies are Christianity, Islam, Psychiatry, Buddhism, Scientology, Pastafarianism, Laveyan Satanism, Marxism and National Socialism (a.k.a. Nazism) and many many others, of course I'm not gonna list all that exist. What is a follower of a polymodular ideology, that can be a can of worms, an object of intense discussion. Here are some approaches (I'll use Islam as an example because it's the polymodular ideology I'm most familiar with, so I can provide better examples) (oh, by the way, I make a distinction between "binary" and "fuzzy" approach... a binary approach is one that says one is either a follower or not a follower of a PM ideology, whereas a fuzzy approach allows degrees of in-between):
1 (binary approach): a follower of a PM ideology is one who adheres to all the modules offered by that ideology. If someone rejects even one module offered by that ideology, then that person is not a follower of that ideology.
2 (fuzzy approach): the higher the amount of modules adhered by a person, the more that person is a follower of that ideology. If someone adheres to all modules of a PM ideology, then that person is a full follower, if someone adheres to none of the modules, that person is fully a "non-follower", and there are many degrees of in-between.
2.1: Each module is of equal importance.
2.2: Modules can vary in importance, so certain modules affect the "score" (so to speak) of how much a person is a follower of a PM ideology much more than other less important modules.
3: (binary approach): modules are classified as either "essential" or "non-essential": a follower of a PM ideology is a person who adheres to all essential modules. For example, for Islam, essential modules may be the five pillars (Shahada, pilgrimage to Mecca, fasting during Ramadan, the charity thing, and the five daily prayers), so with this #3 approach, a Muslim is anyone who adheres to the five pillars of Islam, and therefore, someone who is pro-homosexuality, pro-sex before marriage, pro-polyamory (polygyny and polyandry), pro-alcohol, pro-marijuana etc. can still be considered a Muslim. But not someone who is pro-polytheism, because the Shahada is explicitly against that, since it explicitly says that the gods do not exist (except Allah). However, what is an essential module can be subjective and up to debate, so one can argue anti-homosexuality, anti-alcohol, anti-sex before marriage etc. are also essential modules of Islam.
3.1: A slight variation of this essential vs non-essential module approach is that one can still be considered a follower of a PM ideology if, say, s/he adheres to like 90% of essential modules, as long as that person "compensates" by also adhering to a very large amount/proportion of non-essential modules as well, which is something that can be considered to "fill the void" somehow.
4: (binary approach): a follower of a PM ideology is a person to adheres to at least 50% of the modules of that ideology. How each individual module is counted can be somewhat subjective, however. For example, it can be debated whether a module is one module or two modules etc. when it's a more complex sentence.
x: Other options may be coming soon.
IDEA: emergent modules! For instance, when thinking about atheism, some may think about "scientific rationalism" or "materialism" or something like that. This is merely a historical contigency, since atheism merely states that nothing is divine, that nothing can be considered a deity, (or that there are no gods, if you prefer that wording). "Scientific rationalism" is not a module contained within atheism, but it's an emergent module that arose from historical contingencies.