Yohan Yukiya Seseㆍ사요한・謝雪矢It will depend on the platform. For example, #Friendica (and to an extent #Hubzilla and #Streams), the owner of the group (and anyone else given moderation access) can block accounts. There is also chirp.social which can also block accounts.
Then there is #GNUsocial, which is a rebranded #StatusNet itself a rebranded #Laconica (the first #Fediverse software, c. 2008) have built-in groups feature; which IIRC, can also block users if needed.
Personally, services like Guppe really need to add moderation features, otherwise, what you just described will more likely happen.
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