Is membership in learned societies important in academic career? Countries have different strategies and procedure, but academic career is somehow similar: research publications, teaching, funds, awards. I mean academics do the same thing in all countries to be promoted in their academic career.

However, I see a big difference in membership of learned societies in the US and UK.

UK: Academics care about their status in several societies, Member, Fellow (particularly the latter), and always use the designatory letters after their name: MXX or FXX.

US: Academics only join one or two societies in which they want to be active. Fellow is rare, and no one can directly apply for that, still people do not mention it boldly.

Is really the status of membership in leaned societies important? For example, in academic promotion, research proposals, awards, etc?

Is it useful to join several societies (connected to your field, but you do not have time to be active in all of them) to reach high grade membership? Is it somewhat like an award to be listed in CV?
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.