No, Sir Paul McCartney is not a Christian. Only a person who has been born-again by faith in the Gospel (Good News) of Jesus Christ crucified on the cross, buried, and bodily resurrected the third day is a genuine Christian. That is what the inspired King James Bible teaches (1st Corinthians 15:1-6). YE MUST BE BORN AGAIN! (John 3:5).
In sharp contrast, Paul doesn't believe in the Gospel. If you check online concerning Paul's religious beliefs, you'll find everything from Roman Catholicism to Hinduism to atheism, none of which are Christianity. Perhaps you argue that Paul is private and doesn't share his beliefs. No, has has shared his religious beliefs, which are found all over the internet. Paul has dabbled in everything EXCEPT Biblical Christianity.
For anyone who loves the truth, you fully know that Roman Catholicism is a giant religion completely devoid of truth and God! Catholics trust in their cultish Roman Catholic Church, which teaches Sacramental Salvation (aka, the “Seven Sacraments”). You don't get to Heaven by getting water baptized, confirmed, confessing to a sinful priest, nor any other so-called “sacraments” (a term not even found in the Holy Bible). You have to have childlike faith in the Lord Jesus Christ to become a Christian, which Paul has never once testified publicly. So, no, kindly, by all indications Paul McCartney is going straight to Hell when he dies, to burn forever and ever without hope. I am not happy about that, God forbid, I am simply being very honest.
I admit that I greatly admire Paul McCartney, from a secular viewpoint. I admire his musical genius. The man is clearly a legend to anyone who knows music. I still remember as a boy hearing “Silly Little Love Songs” by Paul McCartney and Wings on the radio in the 1970's. I love music and always have. I play many different stringed instruments (pedal steel, lap steel, banjo, guitar, ukulele, bass, lute and stringed harp). I thank God for music. In my humble opinion, anyone who doesn't like rock music is either dead, weird or a liar! I can hear some sanctimonious self-righteous Christian criticizing me already. Please don't misunderstand, I am 100% against rock music, because it is the number one culprit for the sexual revolution in America. However, it is not a sin to like something. You cannot help what you like or don't like. Being a passionate person who loves music, I like ALL kinds of music!