i dont believe minute men or any other quest in particular causes the crash (at least the crash in monsignor area east of cambridge police station, which is the only one i've experienced so far). the other night i loaded a save at 7.5 hours that didnt crash, the next save was at 9 hours and did have the crash. i proceeding to play out the uncorrupted save for about 2 hours, did the same quests and still didnt crash. the only differences i made the second time around that i can think of is that i took a slightly different route to diamond city, and maybe some other minor things like not getting a haircut in diamond city.
from what i can tell it is something rather random that causes the crash, which would make sense seeing as a small minority of players are experiencing it. which is why i'll probably keep playing that old uncorrupted save and just be careful to make new saves often and check back on the crash area every now and then. unless of course there is a patch that gets released monday after the folks at bethesda's weekend is over. but honestly, the way things are looking i will probably be able to make up the 17 hours or so of gameplay i lost before there is a patch. whether or not i encounter the crash again, who knows, but that other guy said he restarted and has gone 30+ hours on his new save without getting the bug again so that gives me a measure of hope.