What is a religion like when faith is a non-issue?
In many fantasy worlds, there is direct intervention by gods. You don’t need to convince people to believe that your god exists. It isn’t an issue.
How would that change what religious institutions are like?
To a point, we can look to real-world cultures in which the existence of a variety of gods and spirits are accepted as fact. Historically speaking, when a missionary or prophet of an unknown god came by, many ancient (and some less-than-ancient) polytheistic cultures would simply integrate worship of that god into their lives.
In a fantasy world that was inspired by these sorts of cultures – most likely one in which gods are known to exist but not terribly active – most people are likely to show respect to multiple gods, perhaps focusing a bit more on a single god or two whose portfolio includes something related to their trade or lifestyle. Priests and such might be dedicated to a single god, but even this isn’t necessarily the case. If the gods don’t deny each others’ existence, temples might be used to worship multiple gods. Even gods who are enemies might be worshiped in the same temple. Admittedly, some gods might have particular requirements – a nature god might need to be worshiped outside or something.
Now, a fantasy world in which the gods take an active role might be different. For instance, a world in which active worship gives power to the gods might result in either a celestial bureaucracy in which days of worship are carefully (though not necessarily equally) distributed among the gods or active competition between evangelical religious organizations… or some combination of the two.
Alternatively, the gods or their direct agents could walk the land physically. Perhaps they are literal god-kings of nations.
For a different feel, perhaps the devotees of particular gods have organizations dedicated to the portfolio of those gods. This combines worship-through-action with the possibility that gods are concerned less with direct worship and more with the sort of activity that interests them. The church of the god of trade might be an international guild of merchant-priests. The church of the god of war might be a mercenary army. This might get tricky when you get into the area of things like a sun-god, but it could also be pretty cool.