As long as they like the new school better than the old school, it won’t be a problem. That might sound like a stupid obvious response, but I think preparation might be the most important part of a change like this.
My kids, both beyond college age now, both changed schools twice, once during elementary school (same district, different school) and once later, my daughter was in middle school, son entering his sophomore year in high school. All of the changes were made specifically for them, no move was involved in the first, and in the second we moved from the Poway school district to Carmel Valley specifically because of the schools.
We prepared them. They were unhappy where they were. We made sure their were groups for them to participate in before the move happened. And despite my skepticism, all the moves proved to be almost seamless and beneficial. Particularly the 2nd move. Of course there was some stress, but they adapted amazingly fast.