The scholars base their ijtimaa' on authentic Bukhaari & Muslim hadiths:
Narrated from Ibn Umar (may Allaah be pleased with him and his father) that the Prophet (peace and blessings of Allaah be upon him) said: "Be different from the mushrikeen; let your beards grow and trim your moutsaches."
Ahmad and Muslim reported from Abu Hurayrah (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: "Cut your moustaches and let your beards grow; be different from the Magians."
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said:
Fataawa al-Lajnah al-Daa'imah, 5/133"The Qur'aan, Sunnah and ijmaa' (scholarly consensus) all indicate that we must differ from the kuffaar in all aspects and not imitate them, because imitating them on the outside will make us imitate them in their bad deeds and habits, and even in beliefs, which will result in befriending them in our hearts, just as loving them in our hearts will lead to imitating them on the outside."