First up, she said "...would more often than not reach a better conclusion..." which if racist would say "...would always reach a better conclusion..."
Second, her comments weren't some random remarks. She was speaking at a symposium entitled "Raising the Bar: Latino and Latina Presence in the Judiciary and the Struggle for Representation." She talked about her life experience as a Latina women and how it might give her better insight as a judge (and this is important) especially where issues of sex and race are at issue.
Such as on page three she says, "The focus of my speech tonight, however, is not about the struggle to get us where we are and where we need to go but instead to discuss with you what it all will mean to have more women and people of color on the bench." I think that we can all agree that female judges would have better insight into women's issues than men and that a Latina would have better insight into racial cases. That's what she's saying.
And as if the white, Christian, conservative life that Roberts and Alito come from doesn't influence their views, insights and rulings. Just because the white culture is well established on the court and thus often ignored or overlooked versus that of a more fresh culture like that of a Latina women doesn't mean that this white culture still doesn't influence those white, male judges.
A white male judge might be better able to understand certain aspects of things whereas a Latina female might be able to understand other aspects better. What's the big deal? Don't we want judges who have different backgrounds and areas of expertise to reflect the different views within our country? Don't we want judges with different backgrounds and life experiences on the court? To better ensure that issues are considered from many different angles, and to better enable a just and wise decision? It's no different than how we all agree that we need women on the court to bring a woman's touch and understanding of issues that men aren't as adept at dealing with. For example:
Her status [Judge Ginsburg] as the court's lone woman was especially poignant during a recent case involving a 13-year-old girl who had been strip-searched by Arizona school officials looking for drugs. During oral arguments, some other justices minimized the girl's lasting humiliation, but Ginsburg stood out in her concern for the teenager.
"They have never been a 13-year-old girl," she told USA TODAY later when asked about her colleagues' comments during the arguments. "It's a very sensitive age for a girl. I didn't think that my colleagues, some of them, quite understood."
HBW: Sotomayor's speech and the context therein continues and I'll let her speak for herself at this point:
I, like Professor Carter, believe that we should not be so myopic as to believe that others of different experiences or backgrounds are incapable of understanding the values and needs of people from a different group. Many are so capable. As Judge Cedarbaum pointed out to me, nine white men on the Supreme Court in the past have done so on many occasions and on many issues including Brown.HBW: Finally, a key statement at the end of the speech makes clear that she won't simply use her experience as a Latina women to make decisions and will be willing to listen to other view points. As well as work to keep her prejudices in check (as we all must do):
However, to understand takes time and effort, something that not all people are willing to give. For others, their experiences limit their ability to understand the experiences of others. Other simply do not care. Hence, one must accept the proposition that a difference there will be by the presence of women and people of color on the bench.
Each day on the bench I learn something new about the judicial process and about being a professional Latina woman in a world that sometimes looks at me with suspicion. I am reminded each day that I render decisions that affect people concretely and that I owe them constant and complete vigilance in checking my assumptions, presumptions and perspectives and ensuring that to the extent that my limited abilities and capabilities permit me, that I reevaluate them and change as circumstances and cases before me requires. I can and do aspire to be greater than the sum total of my experiences but I accept my limitations. I willingly accept that we who judge must not deny the differences resulting from experience and heritage but attempt, as the Supreme Court suggests, continuously to judge when those opinions, sympathies and prejudices are appropriate.HBW: This context is very important to understanding the snippet that is being thrown around the media and from Conservatives looking to muddy up the water. They don't want you to know the context and that should tell you everything you need to know about Republicans today.