I think its tricky. I'm from England so obviously its a bit of a smaller pool when it comes to cheer. Still, there's always controversy when people move, especially to a bigger gym.
I personally started with a very small team, which then closed down. When I was at university I cheered for the uni team all 3 years. When I was about to graduate I looked at the programmes within travelling distance. I chose the one with the best coaching, facilities and the biggest range of teams. I figured that would give me the best chance of finding somewhere to fit.
I have recently moved gyms again (although ended up sitting out the season through injury). The move was motivated because I was moving area - it was no longer feasible to cheer at the gym I'd been at, as much as I loved them. Again, I looked at the teams near my new location and tried to pick the best fit - I wanted an all-girl team because as a base, all girl suits me better. I wanted to either stick at Level 4, which I had been competing, or push to Level 5. The gym I picked ended up being the one which was nearby AND had a team I thought I'd fit with.
I wouldn't consider myself a gym hopper, because I've never left a gym 'just because'. It's always been for location, or team fit. However, I am certain that some people would class 4 gyms in 10 years as gym hopping.
I guess what I'm trying to say is that in my book, you're only a 'gym hopper' in the negative sense if you leave because of bad blood or to chase a win. If it's logistics or team placement or levels, then fair enough. The old gym wouldn't meet your needs.