ATLANTA — The Georgia General Assembly’s approval of a proposal to strengthen legal protections for opponents of same-sex marriage has set in motion a high-stakes showdown that has drawn some of the nation’s most influential companies into a battle between gay rights activists and religious conservatives.

The bill, which lawmakers approved last week, now faces the scrutiny of Governor Nathan Deal, a Republican. But it is clear that companies and sports organizations, including Apple, Coca-Cola, Delta Air Lines, and the National Football League, will have a significant effect on public debate and the governor’s decision to sign or veto the measure.

Supporters of the bill, which Georgia lawmakers named the Free Exercise Protection Act, say it is a bulwark against pressure for people of many religious faiths to endorse, or at least accept, same-sex marriage.

But to the proposal’s opponents, the bill is a toxic mix of intolerant ideas that was fueled by resistance to the Supreme Court’s decision.

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