Assuming the worst case scenarios where SE is attacked by both trolls & 'legitimate extremists', this would cause more harm then good:
Why isn't X website blacklisted? It's way worse than Y site!
Just one example of a headache caused by keeping a blacklist.
This is especially true when hate groups are involved. If you block an 'I-hate-yellow-people' website, you need to block an 'I-hate-green-people' website.
It might cause headache for legitimate users
For example, the linked post (in OP) has comments asking for evidence of hate groups. If one were provided & was blacklisted, it might cause issues for legitimate users.
Or users who visit hate groups for legitimate reasons (line of work)
It will encourage trolls
Trolls look for responses. If they are suddenly 'black-listed' (and in such trivial way), that will only encourage them.
It will encourage 'legitimate extremists'
Extremists could play the victim. Suddenly SE becomes a 'left leaning website attempting to censor the right'.