I don't think that it would fragment anything, but the opposite. It would make memo a lot better. Personally I don't want to see flat earther crap and spam.
It would only be implemented by services (since the post on-chain cannot be "muted"). True, users would be the ones "blocking/muting" others, but it's only small step to a g-line.
if you have the personal choice to mute people how do you end up at "g-town"? by having your attention on memo now you're choosing to 'mute' the rest of the internet.
I don't have much of an issue with any individual memo client allowing this functionality, but once these blocks/ignores are on-chain they become indicators that can be abused.
True, but memo is the conjunction of two networks: blockchain and humanity. "Muting/Blocking" on *EITHER* side (via miners or popular opinion) endangers this intersection's capacity.