How you deal with the potential negative fallout from your current employer is a difficult situation to handle. Every situation is a little different and what works for you may not work for me. Keep in mind that most employers are going to want a full employment history. They also want extended gaps in employment explained. Above all, the purpose of a resume is to get an interview. Leaving out parts of your employment history could hinder your efforts or disqualify you from getting the interview.
There are a couple of ways of dealing with the contact issue. First, you can choose what information to show on your resume. You can list the company name and city, or just the company name. Whatever you are comfortable with. Our resume builder will ask for the information, but you can select a resume template that does not display it. Second, in an interview or on an employment application you can let the interviewer know that it is not ok to contact the current employer. Be honest and open about your situation. No solution is universal, but following these steps will give you the best opportunity to get an interview and new job.