From their website:
"Congressman Paul Ryan is a strong choice for vice president, and his addition to the GOP ticket will help Republican candidates up and down the ballot,” said R. Clarke Cooper, Log Cabin Republicans Executive Director. “As chairman of the House Budget Committee and author of the Republican “path to prosperity” that provided the blueprint for serious spending cuts in this Congress, nobody is more qualified to articulate a conservative economic vision to restore the American economy and stimulate job creation.
At the same time, Congressman Ryan’s 2007 vote in favor of the Employment Nondiscrimination Act and his consistent willingness to engage with Log Cabin on a range of issues speaks to his record as a fair-minded policymaker. Overall, while Log Cabin Republicans have not completed the endorsement process for the 2012 presidential election, this is a choice that all Republicans can be excited about, and which sends a good message about the kind of campaign Governor Romney wants to run, and the kind of president Governor Romney wants to be.
Not to beat the point into the ground, but Ryan did later revoke his support of ENDA. Does that not impact the LCRs opinion of his "fair mindedness"?