Did any Christians or Jews remain in the time of the Prophet, peace and blessings be upon him, upon the Tawhid (monotheism) and the true religion brought by the Prophets Moses and Jesus, peace be upon them, before the distortion?

There is no established evidence of Jews adhering to the religion of Moses (peace be upon him) at the time of the Prophet Muhammad's (peace be upon him) prophethood. All of them disbelieved Jesus (peace be upon him) and accused him of sorcery, as mentioned in the Holy Quran. As for those who remained steadfast in the true religion during the fatrah (period between prophets), they were Christians, as stated in Al-Tahawi's Mushkil al-Athar. Some scholars mentioned that there were Jews who migrated far away and remained steadfast in Judaism, but this has not been proven with a reliable chain of narration.