I don't know about all of the temple quarters, but the one in the elven quarter in Guldorand isn't like that. An elven favoured soul couldn't own it, it had to be a cleric. A gift of devotion spellsword couldn't own it, it had to be a cleric. A paladin couldn't own it.
Quarters across the entire server are confusing, do not follow the same rules, do not follow the same scripts, have different internal/external doors/signs, have different kinds of chests, different values, some of them can be bidded on and some can't. Some of them you can buy outright, others you can't. Some are guilds with only 1 internal quarter, so people assume that means they're not a guildhouse but a quarter - but the internal quarter can be controlled by the external owner, so the quarter is passed between friends instead of ever open to bidding to the public. Some guildhouses have never been seen by most of the server, have been in certain hands from the moment they went into the server and have not been passed around or even actively used. Some guilds are supposed to have internal quarters full but do not, but that's ok, whilst other guilds are told they need to fill their internal quarters with players.
It is difficult to ask players to report this. It is difficult for DMs to investigate with so many different situations likely to change the outcomes of what is reported.
Maybe quarters / guildhouses / ships need to be looked at again, or at least cohesively updated so that they're all following the same set of rules and systems.