This is not a highly intelligent thing to do, especially for a group whose "About" section includes the following:
I think I'll start a rival group, called something like "Catholics for Catholic Teaching." The purpose of this group would be to issue statements any time one of these other groups releases their typically idiotic statements and pushes their anti-Catholic agenda, and remind Catholics that as Catholics we don't consider the hierarchy "anti-freedom" or, indeed, "anti-anything" when they teach on matters of faith and morals in accordance with the teachings of the whole Church. We'll remind our fellow Catholics what words like "Magisterium" mean (heck, even Wikipedia's got that one sort of figured out). And we'll gently explain that statements like this one...
Drawing on the rich tradition of Catholic social justice teachings, grounded in the Gospel message of Love, American Catholics are among the strongest supporters of equality for lesbian, gay, bisexual, and transgendered (LGBT) people of any religious group in the U.S.
Yet the official voice of the hierarchy increasingly advocates discrimination and opposes reasonable measures to secure basic freedoms for LGBT Americans. Far too often, the anti-freedom voice of the hierarchy is portrayed as representing the moral values of American Catholics. [Emphasis added--E.M.]
Catholics for Equality is a mainstream Catholic organization representing the opinion and attitudes of the very best of Catholic social justice values. We believe that the U.S. bishops are following the dictates of the current Vatican leadership and not the long term values of American Catholicism with its history of fairness and inclusion of all people......are actually heretical, in that the Church's teaching on the grave immorality of homosexual acts (which informs Church teaching on the impossibility of approving gay "marriage" and other notions) is not merely a "Vatican" idea but an ancient and unchanging part of Christian belief.
Of course, forming such a group would, in some ways, be an excessive in futility. "Catholics for Equality" obviously doesn't care in the slightest what actual Church teaching is--they just want to wave it aside as irrelevant so they can approve of the deviancy of the day. It's just too hard to stand with Christ as a sign of contradiction to the world and its sinfulness, especially when you can get in on the trendy approval by making "I'm Catholic, but..." a mantra and a motto.
UPDATE: Larry D has a serious idea to form a group that stands up for real Catholic teaching--see here!