I want certain members of my mumble to have permission to move, kick, and mute other members but I want them to be unable to move, kick or mute admins.
Can I do this with mumble?
Not really. I use a simple approach on my server. I tell everybody I give admin rights to, that if they kick / ban other admins they will be banned permanently themselves. I've run 5 servers for 6+ years without issue.
You could also give people channel only rights. Where they can only mute, move, etc in their channel only.