"Civil rights", if the phrase meant anything at stake in 2008, meant positive rights under state law that were protected by CA's domestic partnership section of its family law code, which an earlier generation of allies (including me) had supported. You could reframe now (post-Obergefell) in federal civil rights terms, but that tells a revisionist account of the history. Back in 2008, state-guaranteed rights were not the issue in front of the citizens of California, and federal bad law (DOMA) was beyond state power to affect.
Remember Obama was also at that time in favor (he said; maybe he was strategically lying but we don't know) of the conjugal definition of marriage.
Yes, I know people find Obama's position then defective and wrong, and some (few) even said so at the time. But I don't see anyone going around arguing that Obama thereby curtailed civil rights, since he supported civil unions or domestic partnerships. If he got off the hook for the "curtailing civil rights" charge by evolving many years later, then what does the phrase mean? It's not a historically or legally accurate description. It's just a rhetorical club to beat up enemies and spare friends.