“Gay people who want to marry have no desire to redefine marriage in any way. When women got the vote, they did not redefine voting. When African-Americans got the right to sit at a lunch counter alongside white people, they did not redefine eating out. They were simply invited to the table. And that is all we want to do. [We... have no desire to change marriage. We want to be entitled to not only the same privileges, but the same responsibilities as straight people.]”
The bracketed sentences were not in the meme, but they are the rest of the quote.
While I agree with the sentiment 110%, this statement is a non-starter for me because it attempts to distract the reader / listener from the elephant in the middle of the room. That elephant is this: change often comes through legal channels. Redefinition occurs because the legal rules are changed. "Any way" includes legal ways.
New legal rights were involved in the aforementioned women’s voting and lunch counter rights. Legal changes are a key way of enforcing change in our divided society. In fact, the legal redefinition of marriage is a major fighting point for opponents of gay marriage.
I dislike any memes like this because they belittle the strident beliefs of a major group. The opponents of gay marriage are very in sync with legal changes. This meme, in one illogical sweeping motion, attempts to win the war by redefining the battle in a way that dishonors all involved.