Why were those who deviated from true Judaism and Christianity attributed to these two religions, even though they introduced things that caused them to depart from their teachings, such as their saying, "Allah is the third of three," and "Ezra is the son of Allah"?

The difference between Islam, Judaism, and Christianity is that whoever deviates from Islam cannot truly be attributed to it. As for Judaism and Christianity, they were abrogated by the prophethood of Prophet Muhammad (peace be upon him). Their names are derived from the actions of their followers, not from the actions of Muslims, and they do not represent the true religion brought by Moses and Jesus.

After the prophethood of Prophet Muhammad (peace be upon him), no one's adherence to any religion other than Islam is accepted. Whoever remains among the People of the Book on their religion and does not believe in Prophet Muhammad (peace be upon him) is in pure disbelief, as confirmed by the words of Allah Almighty: "Those who disbelieved among the People of the Book and the polytheists would not have ceased until there came to them clear evidence. A messenger from Allah reciting purified scriptures…" – until He (Exalted be He) said: "Indeed, those who disbelieved among the People of the Book and the polytheists will be in the fire of Hell, abiding eternally therein. Those are the worst of creatures."

Islam is the religion of all prophets, not merely a name for the followers of Prophet Muhammad (peace be upon him). It has been reported from Qatadah, Al-Hasan Al-Basri, and Mujahid that Judaism and Christianity are innovations and not from Allah. As stated in the hadith of Ubayy ibn Ka'b: "Indeed, the true religion with Allah is the Straight and Submissive Way (Al-Hanifiyyah Al-Muslimah), neither Judaism, nor Christianity, nor Zoroastrianism. Whoever does good will not have his deeds rejected."