The first time the BOS found synths they WIPED out entire cities such as ST. Louis OFF THE MAP, utterly crushed a chapter. And here in the Commonwealth THEY DID THE SAME THING. Synths have wiped out entire towns for resources, abducted people constantly, and basically worked as raiders in the past of the region.
This faction of the BOS is one minded on its hate of anything not human, but the East Coast BOS has never liked non-humans Lyons or otherwise. and have done similiar jobs at the Pitt killing the trogs like mutants.
The BOS doesn't understand synths and think they might be like the Wasteland 2 Synths that can replicate themselves once they leave, or otherwise undermine humanity by sneaking in as spies, and saboteurs. Better to err on the side of caution, if you've ever played wasteland 2 fallout's BOS are doing the same thing, sending a team to investigate a wierd power signature. They believe in nipping the problem in its bud, the institute may have even damaged the BOS over in the east coast to justify the BOS's invasion, Paladin Danse could have been one of many sleeper agents.
The BOS has always treated wastelanders the same, as trash until they become recruits, after that they go through brutal training that can leave up to 80% of the initiates buried 6 feet under before becoming a knight. The Lyons BOS was no different in its distain, however, it was more likely to respect the property of others without resorting to stealing from them usually from what we've seen. However, they did confiscate from the enclave and who knows from whom else perhaps the lone wanderer was simply an exception due to that pip-boy and James.
Keep in mind for all of its extremism the BOS DOES FIX PROBLEMS. They've basically wiped out the mutants in the capital wasteland pushing them into Boston, and are developing infrastructure in the capital wasteland. They're now a true military instead of huddling in the citadel this would suggest a massive increase in number with both the outcasts and east coast working together.
Heck that tiny cult in megaton is now pretty large and significant here in Boston. So in the past 10 years the capital wasteland has grown a whole lot after Elder Max took charge.
Remember that Synths can be reprogramed IN AN INSTANT that means with the right pass code, or frequency the institute can walk in like on Harkness and make him betray his former friends and family, the BOS is right to fear what synths can do to society.
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On the topic, I'm in support of the Minute men because they're the nicest bunch, who show you the ropes, going with them also yields the most benefits with the castle being able to pump out 400 cases of water per day or so, that's 4K caps for doing nothing.
The Institute does not have humanities best interests at heart they simply want to mold the wasteland in their image implanting spies, and sabetours to slowly take back the wasteland. There's no doubt your Son knew where you were, how you were building communities, and after all that his synths STILL shoot you on sight or anyone else on sight. If he cared about YOU, or the Wasteland he would have simply gotten his synths to make communities and protect them on the surface 40 years ago. The Institute would have done THIS 200 years ago if they cared(at least 60 years ago that seems to be when the synth army got big enough to have those skeletons).
The East BOS have that awesomely cool airship, but it wouldn't be wrong to say they're just like the Enclave and would most likely kill any wastelanders that are too irradiated. The Midwest BOS's evil ending has them become like the East Coast in Fallout 4, so there's always the chance the BOS can change since they are slowly progressing to be more accepting, you can even convince the Elder to let Danse go. After that a few years later he might even change his mind on the entire synth problem. With Virgil around, the BOS might even look into curing mutations instead of wiping them out.