An idea is simply something that exists inside your head; you have an idea that God exists, or that people are made of purple cheese, squirrels are all evil (totally), that ZOG or Freemasons secretly run everything, or that doing good things for others will have good consequences. Idea spawns belief when a person decides (consciously or not) that it is has become one, or that they need one for some reason, or when they feel as though they must defend it (no one does - more on that later) or finally, when they attempt to be "right" by collecting information to back up their idea. These last two are the most contentious by definition, as they're the ones that involve other people. More people = More problems, and thank you, Bobby Louis.
There are a lot of reasons people need beliefs. Maybe there's something lacking in their lives, creating a hole, and they can fill that hole with belief in something. Maybe it's a fear of pain or death or loss or loneliness - the classic reasons beliefs are born. Often, for whatever reason, ideas provide no emotional assistance or satisfaction, and beliefs come along to fill the void. In this way, beliefs are good things; an internal construction that helps a person function. Because beliefs are such helpmates in times of need, we become attached to them and feel the need sometimes to share or defend them, and this is when, often, things become problematic. Once the belief is outside of your head, it is vulnerable to the slings and arrows of others, and often, deprived of its raison d'etre and time/space context, a belief becomes not only unbelievable, but laughable - like looking at skinny ties or bell bottoms; hey, made sense at the time, right?
Herein lies the reason why beliefs should likely not be defended, at all, ever - they are eroded in the act of protection. Simply the process of trying to explain this ineffable thing that happened in your head will dilute it, much less parsing it out and guarding it against attacks and questions. In order to understand properly, we literally "had to be there," and no one but you was in your head when this belief happened. Hopefully. The only incontestable reason for belief is feeling, since no one can argue that. It may seem like a belief is strengthened in the sharing, but in truth, no two people will believe a thing exactly the same way, and if they do, they have engaged in groupthink, which is more like viral meme-transmission of an idea involving a conscious decision to think like someone else (or your approximation thereof) and less like actually organically agreeing in totality.
The groupthink phase is typically when people try to be "right" or more often, "correct" about their beliefs. They will want to prove the thing out, if not to you, then to themselves, at least. Therein lies the major problem with most beliefs. Science is based upon observation + idea, where we see a thing and then theorize what might be making that occur, then collecting data to see if we can prove that out. Good science will bail on the idea if the data doesn't back it up. Beliefs, on the other hand, tend to be these pre-constructed mind fortresses surrounding the idea, impregnable to fact, holding up whether there's anything outside the head they were born in to back them up or not. They kind of have to be like this to do their job, and their job is ill-suited for shared reality.
Castles & forts are pointless without people in them, and the people are more important than the buildings - we'd typically tear down a historic edifice to save but one life of a person trapped inside. In the same way, a belief is simply a hollow structure with an idea more important than it is at the core. Principles are much the same. Principles have increasingly become something that people who have them hide behind or inside of, instead of what they probably ought to be; a firm foundation upon which we stand, exposed, when making decisions. Having principles is ultimately a good thing; like tools in a toolbox or arrows in a quiver - one is prepared for what might happen and has some ideas about right action for dealing therewith. One hopes, however, not to have anything break badly enough that one needs a toolbox, and no one would prefer to use arrows to solve a problem. Principles are best kept to oneself and should never be allowed to interfere with even and decent dealings with actual people. If you find yourself not helping a person who needs it "on principle" it might be time to rethink your life.
So, if you ought not share your beliefs and principles can't govern actions, what do we do? How do we do what's right and fix stuff? I would contend that perhaps "we" needn't do anything. Individually, it's on us to engage with what we know needs fixing, and if we can't bring anyone along on that train, maybe we're not supposed to. Leading by example should be all the convincing that is required, because no convincing is required; one simply sees, responds positively, and chooses to emulate. In this way, we cut out the chaff and red tape of things that don't appeal to us, harvesting only the best in forward progress.
Or, you know, such is the dream. Obviously, I'm not trying to convince you of anything.