The Religious Freedom Restoration Act was passed overwhelmingly by the Republican led-state legislature and signed into law on Thursday by Indiana Governor Mike Pence.
Supporters say the legislation will keep the government from forcing business owners to act against strongly held religious beliefs. Opponents say it is discriminatory against gay, lesbian, bisexual and transgender people and broader than other states' religious freedom laws.
"This bill is not about discrimination and does not in any way legalize discrimination in Indiana," said Pence's spokeswoman, Kara Brooks.
That statement did little to meet the concerns of Rick Sutton, one of the marchers: "It's a great sound bite but it's not the truth. I'm not protected. LGBT citizens are not protected," Sutton said. "If we were protected, we would not be there right now."
On Friday, Apple Inc.'s Tim Cook, a Christian and one of the most prominent openly gay American CEOs, joined other executives in criticising the law.
A day after Indiana's move, the Arkansas senate overwhelmingly approved a similar bill, which Governor Asa Hutchinson, a Republican, has said he would sign into law.
In Northern Ireland, a company which refused in May to bake the cake printed with the words 'support gay marriage' because it went against the owners religious views is being brought to court, accused of breaking anti-discrimination laws.