Anita Bryant's son should be able to distance himself from the controversy of his mother's famous stance against gay rights. That was a very long time ago, probably 25-30 years ago, and things have certainly changed in the world since then. The only reason he would have trouble would be if the media continued to bring it up around him and keep it on people's minds.
I definitely think that Anita Bryant's son can escape the controversy of his mother. While it is only logical that people will connect her son to his mother's scandal, people will also be willing to judge him by his own merits. People will know that a person cannot be guilty by association.
Robert Green Jr, the son of Anita Bryant, can easily overcome the controversy of his mother's views. In fact most of the LGBT community would herald him coming "off the reservation" of militant anti-homosexual views. If he is indeed gay, then he would demonstrate that the LGBT community is among us all. If such a person can come out of a fiercely anti-gay home, then they can come from anywhere.
Anita Bryant's son can escape the controversy of his mothers reputation. Sometimes it may be hard if people know who they are and realize they are related but in the end I think that people will see that he is his own person and does not act and do things the same way.
Anita Bryant was a staunch, rigid, anti-gay proponent and sadly, that's pretty much what people remember about her. Her "Rally for Decency" at the Orange Bowl when The Doors performed there alienated people and ended up hurting her singing career. I don't believe her son will ever be able to escape his mother's reputation.