I expect as mentioned you will find more support in PC than among skiers in SLC. But I am guessing that a whole lot of Utahns don't care because the majority don't ski. For what its worth I am a Park City local, live here year round, and I support it. But there is definitely some opposition in PC too. I would say at this time though PC is pretty consumed by what the heck is going to happen with PCMR in general.
Some of the opposition is exactly as stated, LCC and BCC (and backcountry) skiers don't want any more people on their playground. Perfectly understandable.