I like the concept of it, but indeed, it could just spin completely off-trails.
I think time is your best ally. Indeed, changes could occur but in the time scale of years/decades/centuries. YMMV.
Let me illustrate it with some examples.
- Some guy turn up with ideas about brand-new crazy-cool divinity. That guy's pretty good and get some followers, because of good philosophy, maybe a few tricks, sound rhetoric, etc. Then it gathers some momentum, and after a roughly a century, a few thousands people are following the religion, even after the guy's death. Then imperceptibly, the divinity IS created. And as more and more people believe in Her, she gets more and more power or capability to actually do something/think on her own and finally interact with the world.
- Your evil Emperor comes up with his dislike for a minority. Runs his propaganda and so on. Then two possibilities. He finally trip them of power (as Cort Amon mentioned in the comments, look at some examples of how Jews were treated throughout the middle ages), and then got bored and stop his propaganda. And the hatred fades away after a decade. Then nothing happened to that minority. At least nothing remotely noticeable.
- Let's say, on the contrary, that his hatred was a pure racism and not an opportunistic economic/political manoeuvre (it probably makes him a worst politician then), and keeps on blaming them for all the troubles in the world. The population really follow him, and even worse, some of that minority start to believe in it. Generation after generations, the hatred continues and that population becomes really as bad and mean as they were thought to be.
But this is a very crucial point: they are affected by the average thought of ALL who know them. You might say it like this it is their will against the Empire inhabitants will, and pondered by the neighbouring countries inhabitants: do they see them equally bad? Are they neutral? Are they positive?
In a way, the same goes with the Goddess: if some people are convinced that our prophet was just a crackpot, and that no-such Goddess exist, it goes against the effective apparition of the Goddess.
In a word, the effect occurs only if all people related to that thing think, in average, in the same direction.
Another constraint that can make it interesting is the "strength" of the belief. If people merely believe in something without much interest, the effect will differ from if people are fully devoted and numerous. You could have it affect the time for the effect to appear, or how much of the effect actually appears.
As an illustration, if a few tens of people believe in some god in a small region, but don't obsess about it, then maybe the "god"'s power that will appear with time will be just a bit of luck, better weather for the farming, less sicknesses, etc. But if there are hundreds of thousands, with some that dedicate their full life to the god, then it could materialise into a physical being (given enough time).
Effects on Society
Just a few thoughts on how would that impact your societies, I can see a few points that need consideration.
- Gods will physically exists, making clergies very powerful,
- Magic will probably exist as well (at least in some form),
- People within Nations will tend to be good-natured: typically when you want to bind with your neighbours to form a society, you emphasize how similar you are, how good you are, how strong you are together, etc. Those things will BECOME true. If people are convinced that their politicians are good, that will be true, given enough time.
- Due to the averaging and the slow changes, it is unnoticeable by the people and no-one effectively control the climate.
That penultimate point probably need much more thinking, but it depends on plenty of other parameters (tech./evolution level, world, population, etc.) that would make it beyond the scope of that answer.
TL;DR Changes occur only when in average all the concerned population think one way, for enough time.