Musicians are certainly welcome to change their styles. This has happened with many very successful and popular musicians over the years. It doesn't work for everyone, but it never hurts to play around and try different styles and sounds. Some musicians may even find greater success in the new style.
I think that musicians should absolutely be able to change their style. Experimentation and exploration into different styles and genres of music move the entire artistic community forward. Music is a creative profession and musicians are artists. Art is about the expression of oneself through an outlet, in this case music, so confining an artist to a single style or genre prevents this self-expression.
Musicians tend to be creative types, so it should be no surprise that many would like to change their style sometimes. Most musicians will stick close to their roots when it comes to performing the songs that their fans fell in love with. However, at times, musicians may experiment with their music. Some of their fans won't enjoy their new songs as much as the originals. In short, yes, it is okay for musicians to change their style, because fans can still listen to their older songs too.
Musicians are artists. They can create whatever they want, and people who listen to their art don't have to like it. I can understand why fans of a musician's earlier work would be disappointed if the artist changes his or her style, but as a musician, you'll never please everyone, so you should just do whatever makes you happy.