Does peer-reviewing for journals/conferences which advertise to attract reviewers; harm one's academic reputation?
I am hard-pressed to imagine a situation in which reviewing would hurt your reputation. It does pay, as your question hints, to check up on the journal you'd be reviewing for to be sure it isn't scammy, but asking for reviewers isn't much indication one way or the other -- almost every journal needs a stable of willing reviewers, and what harm does asking do?

Yes, editors do choose reviewers for a given paper as carefully as we can, but we mostly haven't the luxury of "who's the most famous person working in this area?" because Most Famous Person is swamped. So we keep a stable of folks who have signed up with us, and we look through it for potential reviewers.