How authentic is the Hadith in which the Messenger says: "If the people of misguidance adopt my Sunnah, then it is incumbent upon the people of my love to abandon it"? And does this necessitate shaving the beard and lowering the izaar (garment below the ankles)?

There is no confirmed evidence that the aforementioned wording is attributed to the Prophet, peace and blessings be upon him. It is established that the Prophet, peace and blessings be upon him, acted upon practices known in the Jahiliyyah (pre-Islamic era) from the religion of Abraham, such as Hajj, circumambulation, and marriage, and the Companions did not wish to oppose the polytheists in these matters. Their opposition, however, was in ordinary matters or innovative acts of worship. Growing a beard was known in the Jahiliyyah, and he did not command opposition to them in that regard.