Jesus Christ is a false god?
No, the Modernists of the Conciliar Church worship another Christ. One who wants "world peace" and the brotherhood of mankind.
Or is He the true God, but you just don't worship Him?
Except the Modernists basically turn God into a big Grandpa in the sky, if the even believe in a deity. Ask yourself why few Novus Ordo priests preach against sin and modern errors that lead or are the result of sin. Their Christ is the buddy Jesus from the movie Dogma.
Because in the passage I just read, JPII worshiped Jesus Christ.
There's a thing called false worship. Unless your of the opinion that all worship is by itself true worship no matter what's being done or said.