Cait's a religious prostitute. Rejecting building a temple to her god causing her not to want to date you makes perfect sense. Shes basically a sex cleric. Also, I dont get why the choice is a big deal. Why would you reject the temple but still want to date Cait?
Because you don't want to spend big money just for endorsing her sexual tendencies?
The real problem with the Temple imo is that there's no alternative options, even a dead end where you rebuild the original temple, receive one item as a reward, and nothing else, would be better than just "Let's build a sex temple, or else it will stay in ruins"
You could even have the option to build it somewhere else in a smaller scale, for example by using where the cult was hiding in the forest
I dunno man, I just feel like putting the temple literally on the middle of the way to the lord's mansion kinda give them a lot of influence, since everyone who would go to the lord would also have to go to the temple too
So unless it's actually the main religion of the lands, it would be better to just not build a sex temple here imo