So recently I decided to start a new playthrough and go with the Minutemen and RR this time, (sided with Institute and then BoS in my first two runs) and I have a quick question pertaining to this run....

If I totally ignore the BoS (outside of helping them at Cambridge PS and clearing ArcJet with Danse), will I have to destroy them as part of either the MM or RR main quests? Or can they be ignored while I focus on eradicating the Institute?

MM no unless you kill a brotherhood main npc like danse.

RR always will happen.

On the Minutemen route:

- MM are only hostile to the faction you are hostile to. In other words, you won't need to destroy the BoS unless you are hostile to them

- since Destruction of the BoS is a unique quest (each faction has their own method of destroying them), I suggest to not skip it

- if you don't sound the evacuation signal while destroying the Institute and then go talk to Desdemona, the Railroad will turn hostile (as you killed all the Synths)

- to enter the Minutemen route, you must be hostile to the Institute. This is easiest done by just rejecting to join the Institute when you meet Shaun, by getting into an argument with Shaun after "Battle of Bunker Hill" or by killing a named Institute character. You can also get into the MM route via the quest Pinned, but at that point you will become the enemy of the BoS

On the Railroad route

- you MUST destroy the BoS and the Institute

- you must not become hostile with the Institute otherwise the Railroad route will fail