In our situation, the ex is a nutcase and it would be worth the inconvenience of choosing a different school to eliminate one more opportunity for drama.
If the ex is not a nutcase, I can see it being workable.
At the end of the day, it's really up to you. Is the inconvenience of having the kids in different schools worth the peace of mind you would gain? I'm not being snarky either; growing up, my brother and I attended a different school in the same city as my stepsister (until high school) and my stepsisters on the other side of the family went to different schools than us even in high school (we grew up in cities 20-30 minutes apart and all wanted to continue school in our respective hometowns). It didn't complicate life all that much, really.
Honestly, it's a big move and big change for everyone as it is. If I knew that *I* would be anxious and worried regardless of whether or not the ex actually pulled any shenanigans, I would just look elsewhere. It's one less thing on your plate in the midst of what's already a big transition.