How do you reconcile that with Judaism? Judaism also claims that God is one and there is no other. Much like Islam.
Jesus was a Jew, and worshipped the true God Jehovah. By Jesus day, most of the Jew's worship had become a mere formalism based upon traditions of men that rendered their worship unacceptable to God. For example, Jesus said the following to the religious leaders of the Jews; "And so you have made the word of God invalid because of your tradition. you hypocrites, Isaiah aptly prophesied about you, when he said, This people honors me with their lips, yet their heart is far removed from me.It is in vain that they keep worshiping me, because they teach commands of men as doctrines." (Matthew 15:6-9) Their hypocritical, formalistic worship led the Jewish nation to reject the Messiah sent by God. I believe the Bible teaches God then rejected the Jewish nation. (Luke 13:34,35)
For anyone to worship Jehovah acceptably, I believe the Bible teaches such worship must be rendered according to his will. (Matthew 7:21-23) Merely claiming to worship the one true God will not suffice, IMO.