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[Only registered and activated users can see links. Click Here To Register...]: Honestly, I don't think that the anti cloak is the problem, I am using it too.
Propably these accounts had either been flagged before or banned because they had been used on a flagged browser.
BP can track you if you had been banned in the past (via Cookie or IP address).
To prevent that, you should reset your router and clear cookies/cache before using a clean account.
You should do that everytime you try to login with a banned account. Otherwise, even a clean account that never had been used with a bot can be lost (See
[Only registered and activated users can see links. Click Here To Register...])
Of course, I might be wrong too. That is just my suggestion.