For example, the Synod on the Middle East issued an official report with 44 propositions. Not once does that document make the claim that the Jews are not the chosen people - which stands to reason, since the Church's official Catechism affirms in paragraph 60 that the Jews are indeed the chosen people.
The article on which this thread is based is an official publication of the SBC leadership and represents itself as the normative position of the SBC, hence the controversy.
Similarly, the official teaching of the PCUSA is one of antipathy to Israel and support of libertinism.
People do not separate from groups like the PCUSA because some individual members and congregations are liberal, but because the leadership's official teaching is liberal.
More likely the congregations/churches will chastise the leadership of the SBC and get them in line if they stray too far — or individuals will change churches to those which don’t affiliate. As far as I am aware the SBC is the only denomination where the power rests with the congregation. Thus, any “official SBC position” which is often breathtakingly quoted by the media as if it is somehow binding on individual churches is laughed off by those in the know as being worth not much more than what’s written on paper since power rests with the individual church congregations. It would take serious heresy being presented by the SBC leadership for churches to leave the organization and unaffiliate. (Disgruntled churches in the past have taken their Cooperative Program funds and sent them to a separate program rather than through the SBC, but they still consider themselves members.)