A systematic review of 47 randomized trials found that cervical manipulation is safe and effective:

• An effect in favor of thrust manipulation plus exercise compared to an exercise regimen alone for a reduction in pain and disability.
• Of the 25 studies (that evaluated adverse events), either no or minor events occurred.
• According to the published trials reviewed, manipulation and mobilization appear safe.  

Coulter ID et al. Manipulation and Mobilization for Treating Chronic Nonspecific Neck Pain: A Systematic Review and Meta-Analysis for an Appropriateness Panel. Pain Physician. 2019 Mar;22(2):E55-E70.