I'd definitely be indifferent myself, as I am to our own military and civil services. I'm more interested in what the many non-humans of the Federation must think of Starfleet, considering so few seem to participate in it.
Indeed, it does make one wonder whether the level of participation and presence of a given race is representative of their a) interest in it, b) their opinion of it or c) their relative power or presence within the Federation overall. I think it's safe to say, for instance, that the Vulcans of Spock's era probably weren't too fond of Starfleet, whereas it's more difficult to gauge in Tuvok's era. Even relatively human-like aliens (Trills, Betazoids, etc.) only pop up occasionally.*
That has always got me thinking that many UFP races regard Starfleet as still an essentially human organization, dating right back to the ENT era. Either that or there are like ten times as many humans in the UFP (which is entirely possible). Also makes me wonder what, if anything, survives of their own space-exploration organizations. We know the Vulcans are still tooling around in their own ships, but what about, say, the Andorians or the Tellarites?
* = Although I believe, as many do, that this is largely a television production conceit (humans are cheap(er)) and not an actual reflection of what the writers intend us to think of the Federation, vis a vis how heterogeneous it is. That's not to say they haven't written dialogue suggesting it's homo-centrism.