It's always kind of concerning when people on one hand say they believe the bible is the word of God and on the other argue that the bible doesn't really say what people post as scripture taken from the bible.
God's elect in scripture predates any denominational teaching. In fact denominations in my view eviscerate the body of Christ. Because men take the truth of the Gospel and then add their take on it, giving their name to that so as to in effect become immortal for having manufactured a denomination that conflates their ideal with God's simple truth.
Then people , as you note when encountering opponents of Calvinist denomination, fight over what is extra-biblical doctrine created by those men the denomination is named after.
God's elect are God's chosen. That's not Calvinist or anyone else. That's God.