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I've grown up through all three major groups, Reform, Conservative (Mostly) and Orthodox. I can assure you the only groups of people who even USE the word are Orthodox. Goyim is a Yiddish slang word for gentile.
Most Jews don't have issues with non-Jews as long as they aren't assholes. Typically most don't think lowly of others even if they aren't Jewish because we make up such a small percentage of the world's religious population that it's the only way that we can really branch out. You'll sometimes get really closed-in people though.