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Long nails are fine and safe for you to have when using a menstrual cup, period. You do need to be careful to not scratch yourself during the process of insertion, but taking insertion slow and steady will help you in this matter.
Additionally, it is important for health and hygiene reasons that you wash your hands and underneath your nails to certify that you do not transfer any bacteria from them to your lady parts which can cause infections, irritation, and discomfort.