Does telling a future employer not to contact my current employer look bad?
No, not even a little bit. A prospective employer will understand that you are currently holding down another job and that you have not told that current job you are looking for a new job.
Most jobs don't contact past employers anyway, because in today's world the employer really can't say much of anything without the threat of being sued by the individual they are discussing. Typically VERY generic stuff if they were to call an employer.