Is membership in learned societies important in academic career?
Even in the U.S., it will depend very much on the field you're talking about - it differs widely even for fields that might be considered adjacent to each other.

For example, I'm an Epidemiologist. While professional memberships might rate a line or two on a CV (I use them as another way for people keyword searching for people 'like them' since I straddle a couple fields), and there definitely benefits to being a member and certain recognitions from societies might help in the "building a reputation" component of many tenure/promotion cases, there's not necessarily much listing of those unless it's a very big deal (AAAS Fellow, National Academy, etc.). My major professional society doesn't even have fellows, just the occasional award or committee position.

However, in academic medicine, where many of my collaborators are, this is very different. For example, it's very common for them to list "FXXX" or "FYYYY" as part of their "full" title, fellowship is a much bigger deal, and there is a clear application process.