I think that most people today have forgotten about the Matthew Shepherd case, so I'm not sure how much it affects today's views. Certainly, for those of us who remember what happened, it has an impact. HBO had a great show on called "The Laramie Project", which starred a lot of Hollywood heavy hitters. It was a very emotional and touching movie, and I'd highly recommend it. I was young when this incident happened, but I remember it really affecting me, and after I watched that movie, I realized how absolutely terrible it is for someone to be punished with death based solely on one's sexuality. It's just wrong. Many people, after the incident, did not see it the same way I did. Some actually think that homosexuality should be punished with death. Some are totally ok with discrimination against gays. However, I think Matthew's death brough gay rights to the forefront of the political agenda, albeit temporarily.
I would guess that most people, sadly, do not know who Matthew Shepherd was. When this case was made public, the brutality of it shocked the American people and put a human face on anti-gay discrimination and violence in the US.
If it did anything to change Americans' views, I think it introduced them to the idea that our society was too tolerant of discrimination against homosexuals, and it also raised their support for the idea of hate crimes legislation. In terms of its affect on the gay population in America, it motivated them to get organized and to put increasing political pressure on our government at both the state and federal level for hate crimes laws and legal equality for gay citizens.
I would say that the Matthew Shepard case (which I do not think has much of an impact today since it happened 12 years ago) helped to polarize the United States on the issue of gay rights.
For people who advocate gay rights, Shepard's case was a wake up call. Because of it, there was a great push for laws against hate crimes. A law named after Shepard that makes such crimes federal crimes just passed last year after years of efforts.
The push for more protection for gay rights helped to cause a backlash against them. Gay rights are now much more of an important issue on the US political scene.
Not all of this came about because of Shepard's murder, but it was certainly a catalyst that brought gay rights farther up on the national political agenda.