The operative phrase in 1988(b) is "prevailing party". A moot case has no prevailing party.
Right, that's the operative phrase. In the absence of a final decision on the merits, it's not always clear-cut that you have a prevailing party. There have been some cases solely about legal fees in situations where someone files a civil rights case and the other side promptly does what is being demanded, so there's no case left to try. The plaintiff's (possibly ACLU) lawyers still want to get paid, saying that but for them, the "abuses" would have continued. Some cases hold that no fees are appropriate in such situations.
There is language in such cases that to be a prevailing party, there has to be some court action in your favor -- perhaps a court-approved settlement or at least some kind of court-ordered relief. I think those are employment discrimination cases. They may not apply here; I really don't know. It's all a bit murky.
But here, after a six-week trial, and after it's been shown that the school board had lied about important issues (motivation, source of funds for their Pandas book, maybe some other stuff), and after both sides have put on their entire case and rested, I doubt that one side could avoid paying legal fees just by dropping the behavior that triggered the suit in the first place. I don't think there's any case about legal fees in that situation.
The school board was probably correct to conclude that they couldn't escape liability by dropping the ID stuff at that late date. Besides, even dropping the ID nonsense wouldn't have ended the case. The plaintiffs wanted a permanent injunction, not just a temporary fix. The school board literally couldn't have ended the case by themselves, unless they consented to such an injunction, and then -- of course -- there would have been a prevailing party.
However, if the Discovery Institute wants to blame the whole mess on the ACLU and the new school board, it won't be the first time they've twisted things around. In fact, I'd be amazed if they ever told the truth about anything.
Simply withdrawing the policy would not have mooted the case. They were seeking injunctive relief, which would have continued, post-policy change, and there is a theory in the law (the specifics escape me, now) that essentially says that a state party can't defeat the "case and controversy" requirement by withdrawing the unconstitutional act. It's considered moot, but capable of being repeated, and, therefore, a controversy does exist.