All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Allah, The Exalted, is our Lord and the Lord of the Jews and Christians, and He is the Lord and Master of all things. However, the worship of the Jews and Christians dedicated to Allah, The Exalted, is invalid and will be of no avail to them on the Day of Resurrection because it is marred with disbelief in Him and ascribing partners to Him. They disbelieved in Him when they ascribed attributes of imperfection to Him, disbelieved in His Messenger Muhammad associated partners with Him in worship, and took their rabbis and monks as lords besides Him, obeying them as they declared lawful what Allah has deemed unlawful and declared unlawful what He has deemed lawful. Allah, The Exalted, Says (what means): {And most of them believe not in Allah except while they associate others with Him.} [Quran 12:106] Al-Aloosi said in Rooh Al-Ma‘aani, interpreting this verse: “It was also narrated on the authority of Ibn ‘Abbaas that it refers to the People of the Scripture who believed in Allah, The Exalted, but associated partners with Him by disbelieving in His Messenger Muhammad or by worshipping ‘Uzayr and ‘Eesa (Jesus), may Allaah exalt their mention.” [End of quote]
Shaykhul-Islaam Ibn Taymiyyah said: “The Jews and the Christians say, ‘We worship Allah!’ They think that worshiping Him while associating partners with Him is valid worship, and they are liars in this respect.” [End of quote]
The bottom line is that the deity worshipped by the Jews and Christians, in principle, is Allah, The Exalted, but when they marred their worship of Him with Kufr (disbelief) and Shirk (ascribing partners unto Him), their worship became invalid.
Allah Knows best.