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If their new policy is that they only accept automatic withdrawals then you do not have any options because they will not allow you to pay in any other way.
For now, I suggest that you send them a letter and set out a clear explanation as to why you do not want this to happen. Perhaps they will agree, but if not your only option would be to open a second bank account, perhaps in a different bank if you feel that would give you more security and privacy.
Does that help as a starting point?