Being rich and famous is not sinful. However, any obsession with anything other than God is sinful and is displeasing to Him. Jesus taught against greed and commanded us not to store up treasures on earth, but in heaven.
The Bible has many warnings for those whose life ambition is to be rich. Being greed especially with material wealth has a way of taking our eyes off of what’s important and eternal. We should not make fame and fortune a primary pursuit in life. Rather, we should make glorifying God our primary goal.