Beehaw is sending a message, imho, that instances need take reasonable measures to ensure their users don’t repeatedly commit some sort of abuse.

Do mods even have this kind of power? Can they see what their users are posting on other instances?

For that matter, I don't know if this is so much a statement being made by Beehaw about quality of users as it is a necessary step for their moderation style. I think Beehaw has very strict mdoeration policies and they're just having a hard time keeping up with their own influx of users let alone LW and SIJW who have open registration.

In their own words

This is also not a permanent judgement (or a moral one on the part of either community’s owner, i should add–we just have differing interests here and that’s fine).