Hmm.. The fallout 4 BOS are kinda dicks and Arthur Maxon is the biggest dick of them all.They just go around and hoard tech just like the mojave chapter with no regard for the lives and troubles of the average wastelander.I think elder Lyons was steering the BOS in a better direction althou it conflicted severly with their original objective to get all the tech they can.It would have been nice to have the brotherhood make an exception and relax their doctrine in order to be able to lend some help to the wasteland and maybe make a better name for themselves.This way they would be able to get more conscripts and it would be easier for the other ppl to accept them in their settlement and maybe even be at ease with them around.
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I usualy just go in shooting and let someone else sift through the ashes to figure out what was going on.

Well regarding the BOS... atleast they are not the Institute.. who I really compare to Nazi's..

1.  Institute Conducts Experiments on unwilling test Subjects... Nazi's conduct experiments on unwilling test subjects.

2.  Institute is rounding up Civilians from the commonwealth to kill via FEV tests and just to kill because they are there.... Nazi's... rounded up Gypsys, Jews, Russians... everyone non them.. and killed them.

3.  Institute is working to replace all non institute persons with Synths as the rest of the commonwealth is worthless, (Institute NPC's are talking about wiping out the surface so they can start over)  Nazi's wanted to wipe out pretty much everyone who isn't them and doesn't agree with them.

4.  Institute is trying to erase free will via limiting knowledge to themselves and creating Synths as the surface race who are blindly loyal to the institute...  Nazi's book burning extravaganza...

5.  Institute hunts down Synths that don't agree with them, killing or mind wiping them for disagreeing with the Institute Policies.  (Hence the railroad exists to protect them and their right to have a will and life of their own)  Many Germans were also afraid of the Nazi Party but feared for the lives of their family and withheld their opinions out of that fear.

So now.. the BOS..

1.  Don't care about saving people but they are rather focused on keeping technology out of the hands of people like the Institute who do things like... Experiment on people with FEV for the heck of it, use new weapons and FEV to wipe out the surface dwellers.  Replace people with synths so they can be better controlled...

2.  Shoot at but not hit NON-feral ghouls who come to close to scare them away...

3.  Kill Feral Ghouls

4.  Kill Super Mutants.

5.  Can be reasoned with(Elder Maxon) to spare synths (Paladin Danse).. there is no reasoning with the institute...

6.  Require aid of the people of the commonwealth to help defeat the institute such as quartering soldiers if need be, and giving up extra supplies for the war effort against the institute.  (Proctor Teagan's quest Feeding the Troops, I just either pay or charm them into helping me get the food, its like the military.  Commander gives you the mission, you have to come up with the best way to accomplish it in accordance with the best interest of the Commander and the Organization, it only goes to prove that not pissing off the locals would be the best choice)

Yes the BOS isn't here to win hearts and minds in FO4 like they were in FO3, they are here to defeat the Institute and the Super Mutants... Super Mutants have been the enemy of the BOS since FO1..

Gyrard Hit the nail on the head on this one. You can dislike someone, and you can tell someone you dislike them... That happens alot.. but systematically killing Everyone who isnt you, is what makes the Institute like the Nazi's