SQl Sever Backup Exclude Users
Unfortunately no, you can't exclude anything from a backup.

If you are talking about Windows Logins then it probably isn't that big a deal.  The SIDs won't match anything on their network (very unlikely anyway) so all they will have is the usernames without any of the permissions associated.  SQL Logins of course will work fine as long as they create a login to match the users.

The only ways I can think of to avoid having the users in your DB when you do the backup are going to range from annoying to difficult.  Basically you either create a copy of your DB that you keep up to date but doesn't have any of the database principals you don't want or you script out all of the permissions, drop them, run the backup, and re-create the permissions.  Of course I wouldn't try that second option during the business day.