Keeping Nails Long
No we as Muslims are not allowed to keep long nails. This was Sunnah established by the Prophet (SWS) and falls under Customs and Etiquette . It is a highly emphatic sunnah ( Sunnat-e-Mokada ) but cannot be called Farz or absolutely haram. Please refer to the following responses of Ghamidi Sahab : Discussion 71403 • Reply 71431 Discussion 71403 • Reply 71432
Brother Umer, I feel like your answer says you cannot and you can at the same time. If it is not a Fard to keep short nails, then long nails can be kept. If it is Sunnah to keep short nails and it is not a religious order from Allah then it is just related to person hygiene that prophet Muhammad followed. Now a days long nails can be kept clean so issue of hygiene may not apply.
It is a religious order recived through the most credible means of transmission namely, ijma and tawatur. Religious directives are of two caegories i ) Farz ii ) Recommended ( Mustahab ) For the second category direcetives received as Sunnah, some are very emphatic like the ones that belong to customs and etiquettes including trimming of nails. The reason they have been instituted as religous directies is for Muslims to follow. The only question that arises is what if someone fails to follow any of these, would it be same as ignoring a farz directive? Then answer to this question is no, it is not same as farz and neither are implications when someone opts to not do it. An example to understand this point would be Eid Salah, which is a highly emphatic Sunnah, but it is a Mustahab act and if someone does not perform it, would not be held accountable.