I partially agree with Matthew here- but I feel like you shouldn't have to work to keep things "separate".
I haven't had much experience- but maybe it's best just to be civil to everyone, even those who don't return the sentiment. If you make friends, you make friends. If you stay distant for the sake of focusing on the task at hand, so be it. So long as you understand that business is business, and everyone is there to do a job, then the issue of "friendship" shouldn't matter so much.
On the one hand, I've got friends in a cast who listen to what I have to say and more-or-less follow through on what I'm asking them to do. On the other hand, I've got friends who try to use our relationship to take advantage and weasel their way out of working. It's this hand that you have to worry about- especially in high school. Not everyone understands how important a show can be to a stage manager- for many kids, it's "just a high school show". When performers start abusing your relationship with them, it's time to draw the line.
Case in point though- if you're civil with everyone, then your reputation is likely to proceed you. Be fair, but not brutal. Focus on running a smooth and efficient show, and everything else should fall into place.
Best of Luck!