Reasonable Marxists may disagree on the class status of the Bagginses:
https://users.pfw.edu/wootdm01/bilbo.html
Personally I think that as well as their local status, their class can also be analyzed from a global perspective, where the hierarchy of the wider world goes Eru > Ainur > Maiar > Eldar/Edain > Other Men/Elves > maybe Dwarves > everything else including Hobbits. In global Arda it matters not that Frodo was amongst the wealthiest and highest-status Hobbits - they are viewed as marginal by the other races, and it was this very marginal status that caused the “higher” races to overlook their potential, which is a large part of how they succeeded.
I’ll also defend the idea that the military strategizing of Great Men was for nought. We are told quite clearly that the ring is the only hope for free peoples; that even if it is kept from Sauron, his forces will inevitably win. The Elves recognized this hopelessness (as part of the overall decline of “magic” in the world) and were slowly abandoning Middle Earth. Aside from Aragorn and possibly Faramir, the ruling Men are depicted as weak and flawed. The elite Elves and Men had ultimately failed - even after defeating Morgoth, Sauron had prevailed; even after defeating Sauron, he had returned. Further battle was positioned as noble but most definitely fruitless, unless the ring could also be destroyed. The greatest contributions of Men are taken to be those that assist or buy time for the Hobbits. No, they’re not taken to task for this multi-generational failure, and royal birthright prevails, but then Tolkien as a Catholic wasn’t aiming to demonstrate anything about class liberation - hence my reading of the story as being one of cross-class collaboration, and the wider point being that achieving meaningful change is likely to involve “big people” and “little people” finding ways of working together.