There were many heavy opponents to gay rights early on. Anita Bryant was one, as well as Jerry Fallwell. The louder people spoke out about gay rights, the more people stood up for what was right in the belief that everyone was equal and should be treated as such. When you throw in the religious aspect of it is like two prize fighters squaring off. People will pay attention regardless of what side they are on.
Anita Bryant's heyday was in the mid-1970s. That was when her crusade against Harvey Milk's laws in San Francisco was brought to the center of American civil rights. Because of Bryant's pro-Christian, anti-gay banter, her opponents were able to galvanize even quicker. As such, Milk's law withstood any protests and was able to stay on the books as some of the first pro-gay legislation in America.
I do not believe Anita Bryant's protest of the Milk Law helped bring gay rights to the forefront of culture. In her time, opposing such laws still hurt her career but the world still had a lot of closeted homosexuals and it certainly wasn't a common site in society. I think it took many years for people to adjust to the fact that this orientation was real and its taken many more years for people to become more comfortable with it. If anything, Anita Bryant hindered the movement.
People often get these things confused - the protesting of something that brings attention would not bring attention if the issue was not already at the forefront of thought for the people. This is an important distinction to make - the issue is already at hand, and people are hyper snsitive to it.
No, I do not think that Anita Bryant's protest of the Milk law has helped bring gay rights to the forefront of culture, because it would have risen to the forefront of culture anyways. It is not any one particular thing that has brought the gay rights issues. Rather it is individual people speaking to their loved ones and their communities.