most tap water will have a chemical taint which cats can smell more clearly than we can. That is why they prefer to drink water from various holes in the ground, and bowls outside. Having moved to London from New Zealand, where the water is pumped directly out of the ground into your water mains, the difference in taste in London (and subsequently Chatham) water is enormous. The water tastes dead and lifeless, rather than vibrant and mountain spring-ish.
So probably your cat is showing a more discerning palate rather than anything more worrying
The hot weather will cause cats to drink more frequently. I know mine are doing so, but then, so am I.
Unless she is showing other signs of cystitis I would let her do what she is most comfortable doing. At least she is getting fluids, which is very important to cats whether or not they have cystitis.