Cait's buttginity is not related to whether or not you help her construct Catte Temple, at all. Once you complete the Cat Call quest she'll talk with the Champ about it (assuming you have a penis or ghostlight) the next time you access her sex menu, completely independently of anything you do with the temple. They're only connected insofar as finishing Cat Call is
also the trigger for Salwah to show up.
Constructing the temple does have an influence on Cait because it has an influence on her future, as both she and the narrative text notes. It will tie her down to both the Marches and her religion and since you're basically constructing a high-class brothel and putting her in charge of it, that affects her character as well since it's encouraging rampant turbosluttery. See Alypia's comments
here for more on that topic. If you don't construct the temple, that means her future is much more open and she's not necessarily tied down to doing the Mallachite Thing. This is... kind of obvious, I'd think. It's entirely optional but that doesn't mean it's a choice without
consequences; this is why the game tells you very directly when you're asked to make the decision that building the temple will tie her down for years to come.