if i had a dime for every time i innocently said something that was misinterpreted and hurt someone else's feelings, i wouldn't have to worry about my ssd check arriving on time! we all do it. it's part of the human condition.
when people are native speakers of the same language, they filter each word and syntactic element through their individual, idiosyncratic, background. this includes their ethnic and social heritage, their religious heritage, ... it goes on and on. we operate in an area known as "the common core of shared meaning" which is where elements of the speaker's heritage overlap the listener's heritage. this is a relatively narrow spectrum and it's a wonder that any of us can understand each other.
each and every person (except me, of course) operates socially in a context of wanting to be accepted and recognized as being "part of the group." your sil denied you this space. it hurts.
would i go back and try to make nice? i'm, as you know, "different." but the suggestion of laying all of the cards on the table and clearing up the misunderstanding, at least in theory, provides room for growth.
hope this helps.