To Current Matters (Alliance)

Fairly easy to obtain:

Make a new character and choose to level in BfA and finish all 3 outposts and any other quest on your ship before hitting level 50!
Once you are level 50 accept A Dying World from [npc=154464] (alliance) or [npc=154465] (horde). Apparently horde and alliance got the same quest id for it.
After accepting A Dying World just complete the follow up quests The Heart of Azeroth > Infusing the Heart > A Brother's Help > Stubborn as a Bronzebeard > Necessity is the MOTHER and A One-Way Ticket to the Heart until you finally get To Current Matters or To Current Matters

Tried it several times, works 100% if you make a new char which dont got [item=158075] yet.

Wanted to add my piece that I've attempted/tried to get this quest: To Current Matters, in this order:

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• Got to L50, Freeze XP
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• Got 3 Outpost completed (tried 2, quest didn't appear, finished 3, it did)
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• Do, A Dying World -> The Heart of Azeroth -> Infusing the Heart (got neck), don't do any other neck quest
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• Did Trig Sound campaign (from Nath "The First Assault")
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• Picked up quest from Nath, A Stroll Through a Cemetery (but did not do it), then A Brother's Help was available from [npc=136907] in Silithus
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• Completed A Brother's Help then To Current Matters was available..
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Side Note: DO NOT do Send the Fleet for Nazj chain/openings, which boost your neck to L50, and you're screwed

For my max level (70) alt, never done any BFA content, and without the HOA. This is my experience and taking from both @arleniaa and @Vandiel01 posts:

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• Pick up Intro to BFA starter quest beside the Warboard in SW/Org, Battle for Azeroth: Tides of War/Battle for Azeroth: Mission Statement (take 2nd quest but don't do, talk to quest giver again who then offers skip which you need to take)
  
• Once Intro chain is done (Achievement is granted (Come Sail Away/Welcome to Zandalar at the end of the chain)
  
• Then use the Scouting Map to pick a starting zone - this must be done to trigger the war campaign.
  
• Ally: Go to the boat (Genn Greyman-The War Campaign) Horde: Great Seal (Nathanos-The War Campaign, start the war campaign, and complete the 3 zone outpost chains. As noted: do NOT do Send the Fleet!
  
• A Dying World should then be offered by Earthen Guardian in Boralus/Dazar'alor. If it isn't, as noted by @kajimelons, under A Dying World, for DF toons, make sure you've completed the DF intro quest To the Dragon Isles!/To the Dragon Isles! (maybe some day this will get fixed)
  
• For my level 70, I was offered A Brother's Help immediately after doing Infusing the Heart from above chain
  
• Complete the 4 quests in A Brother's Help chain and then Magni offers this quest in the Chamber of the Heart.
  
  UPDATE: Didn't seem to be able to get this to work for my horde-if anyone was able, please add comment with details!