There is no reason why multiple factions cannot have the same or similar ideology (or policies) with respect to a particular environment or interaction traditions, but be different in many or even most other respect.
If you think this cannot be the case, then I recommend you consider the case of several business execs in the same room from different companies and having different agenda and all disagreeing on everything except one thing - that their environment of wheeling and dealing is the best environment. So they have a common cause - the market. Maybe they would all have different names and logos, but the would still have that one thing in common and thus could, when opposed by some other group (like say government seeking to impose stronger regulations), rally together for that one cause.
Similarly, an Independent is someone who thinks in terms of independence. We might use different faction names (in-game or not), but they all believe in their own independence. If faced with an outside threat, they might seek allies among other's who are independent-minded, even if their particular ideologies (communist, capitalist, confederate, federalist, etc) may be quite different. Allegiances are formed along as many different lines as players can think of.
For my own part, I support any and many independent democracy faction I see in my scope of game play. If we are against a superpower, say, then we might seek allies among other independents, even if they were totalitarian. An independent dictatorship faction is preferable to an imperial patronage in ALD space - because it works against ALD by making her players' control costs increase, thus requiring a greater work load to fortify a control bubble. I'll work with 4F (Fighters for Forlorn Freedom [Imp-Dict]), for example, if I must, to resist ALD's (ALD hates (read: is weak against) dictatorships) control of a control bubble. I'd prefer to work with other democratic (or social factions), but politics makes strange bedfellows sometimes.
When it comes time to oppose the tyranny of a superpower, independent factions may well rally with each other to defend themselves, but also be entirely devoted to their own autonomy.