There's another interpretation, which is "the sorts of things that LW groups do affects whether I participate in LW communities [in the sense of particular local groups] and thereby the extent to which I participate in the greater LW community [in the larger sense of "people who identify as 'LWers' and do things collectively on that basis]".

After all, if I want to engage with the larger LW community, the most direct (and one of the most feasible by far) ways to do so is to participate in your local LW community, should such exist. One can hardly choose to participate in some other local LW community that is located in Whatevertown, Distantstate.