You get access to their quests and unique merchants if you help. But if you decide to not help is there any benefit?
Thanks.
Ana drops a unique Blue and Purple hood, and Barrow unlocks a nem boss once you get them to max negative rep. Both also unlock a dungeon area, though I usually just side with them both every play through.
Generally there is a zero reasons to be foe with this faction
Anasteria - she could drop their helmets, that’s all (helmet also could drop in crucible, so there is no sense at all to become hostile with Anasteria)
Barrowholm - pretty much same as Anastiria, if become hostile with them you will fight with most dangerous nemesis in whole game - with Reaper of the Lost
Roleplaying. That is pretty much the only reason to go against them. And yes, Ana’s helmet or Reaper’s pantsu 
Reaper is just a much weaker, discount version of Ravager 
He’s the Ravager’s cousin Carl, he tries but he’s just not there yet.
Resper of the Lost, also known as Ravager’s semi retarded cousin
The rule of thumb with GD is that you usually just miss out on content if you decide to kill people instead of spare them.
It’s always a good idea to have at least 1 toon with Anasteria and Barrowholm at Nemesis for their unique MI’s (Outcast’s Hood and Secret and Reaper’s MI Leg armour). You can get them in Crucible but Crucible isn’t for everyone and what items you get are totally random (as in you can fight Reaper in the Crucbile and have 0 Leg armour drop) so at least you can farm the mobs specifically and pray for good rolls.
I have read boss-specific legendaries don’t drop in Crucible. Lies?
Does it require Nemesis with Anasteria? Is it even real to reach such a low reputation with these minor factions?
Nope, I got one Anne Hood and one Decree of Aldritch in Crucible. Only Sharzul and Garbabol MI cant drop.
Ahh forgot, both Log and Theordin MIs too.