In my opinion, it is virtually impossible for a celebrity to undergo anything that can be termed an issue in a relationship without that issue becoming public knowledge. I am not saying those issues should be dug for but that it is fine if they are learned. When a celebrity pursues a career as a celebrity, they seek the limelight, good or bad.
No, celebrity's personal relationship issues should not be made public knowledge. By definition, those relationships are personal and should be kept quiet. With few exceptions, relationships have nothing to do with the celebrity's job. Many celebrities use their issues for publicity which is shameful, but the real concern is those who don't intend to make their issues public. It is totally unfair for us, the public to insist on knowing about these gossip situations.
Think about it, if you had a break up or an incident with someone in your personal life, would you want that to go public? All people would do is start trouble so they can watch some drama unfold and besides, wouldn't you rather deal with those kinds of problems without the whole world knowing about it? Your personal business should not be a spectacle for others to watch for their own entertainment, celebrity or not.
No, I don't believe a celebrity's personal relationship issues should be made public. Celebrities should have the same right to privacy like every other citizen. If the celebrity is not doing anything illegal or harmful in their private life, then he or she should not have the problems exposed. Even though the work they do is public, this openness shouldn't extend to personal life.